Abstract

We present a theoretical and experimental comparison of single-tone and two-tone frequency modulation (FM) spectroscopy using lead–salt diode lasers. Our analysis reveals those diode laser operating characteristics that are necessary for high sensitivity performance using either technique for IR absorption measurements. High sensitivity performance using these techniques requires laser diodes having low incidental amplitude modulation and a small variation in FM/AM phase shift over a suitable diode tuning range. Neither requirement is met with the present mesa-stripe lead-salt diode laser technology.

© 1987 Optical Society of America

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References

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  1. M. Gehrtz, W. Lenth, A. T. Young, H. S. Johnston, “High-Frequency-Modulation Spectroscopy with Lead–Salt Diode Lasers,” Opt. Lett. 11, 132 (1986).
    [CrossRef] [PubMed]
  2. D. E. Cooper, J. P. Watjen, “Two-Tone Optical Heterodyne Spectroscopy with a Tunable Lead–Salt Diode Laser,” Opt. Lett. 11, 606 (1986).
    [CrossRef] [PubMed]
  3. G. C. Bjorklund, “Frequency-Modulation Spectroscopy,” Opt. Lett. 5, 15 (1980).
    [CrossRef] [PubMed]
  4. G. R. Janik, C. B. Carlisle, T. F. Gallagher, “Two-Tone Frequency Modulation Spectroscopy,” J. Opt. Soc. Am. B, 3, 1070 (1986).
    [CrossRef]
  5. D. E. Cooper, R. E. Warren, “Two-Tone Optical Heterodyne Spectroscopy with Diode Lasers: Theory of Line Shapes and Experimental Results,” J. Opt. Soc. Am. B 4, 470 (1987).
    [CrossRef]
  6. G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  7. M. Gehrtz, G. C. Bjorklund, E. A. Whittaker, “Quantum-Limited Laser Frequency-Modulation Spectroscopy,” J. Opt. Soc. Am. B 2, 1510 (1985).
    [CrossRef]

1987 (1)

1986 (3)

1985 (1)

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

1980 (1)

Bjorklund, G. C.

M. Gehrtz, G. C. Bjorklund, 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, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

G. C. Bjorklund, “Frequency-Modulation Spectroscopy,” Opt. Lett. 5, 15 (1980).
[CrossRef] [PubMed]

Carlisle, C. B.

Cooper, D. E.

Gallagher, T. F.

Gehrtz, M.

Janik, G. R.

Johnston, H. S.

Lenth, W.

M. Gehrtz, W. Lenth, A. T. Young, H. S. Johnston, “High-Frequency-Modulation Spectroscopy with Lead–Salt Diode Lasers,” Opt. Lett. 11, 132 (1986).
[CrossRef] [PubMed]

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency Modulation (FM) Spectroscopy: Theory of Lineshapes and Signal-to-Noise Analysis,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

Warren, R. E.

Watjen, J. P.

Whittaker, E. A.

Young, A. T.

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Figures (10)

Fig. 1
Fig. 1

Variation of the sensitivity in two-tone FMS with FM index β for AM indices M of 0, 0.01, 0.02, and 0.03 using the standard system parameters given in the text.

Fig. 2
Fig. 2

Variation of the sensitivity in two-tone FMS with AM index for β = 1.15 and various laser powers.

Fig. 3
Fig. 3

Variation of sensitivity in single-tone FMS with FM index for AM indices of 0, 0.01, 0.02, and 0.03 with δψ = 2° and using the standard system parameters.

Fig. 4
Fig. 4

Variation of the sensitivity in single-tone FMS with AM index for β = 1.1, δψ = 2°, and various laser powers.

Fig. 5
Fig. 5

Single-tone FMS sensitivity dependence on diode laser/ local oscillator phase difference δψ for AM indices of 0.001, 0.01, 0.1.

Fig. 6
Fig. 6

Comparison of single-tone and two-tone FMS sensitivites as a function of AM index for P0 = 300 μW, δψ = 0 and 2°.

Fig. 7
Fig. 7

Single-tone spectra from a Doppler-broadened transition near 930 cm−1 with the local oscillator phase set for (a) maximum positive background, (b) zero background, and (c) maximum negative background.

Fig. 8
Fig. 8

Theoretical single-tone spectra from a Gaussian line shape generated using the equations given in the text with β = 1.0, M = 0.1, ψ = 30°, α0 = 0.15, and νm/γ = 7.3 with the local oscillator phase adjusted for (a) maximum positive background, (b) zero background, and (c) maximum negative background.

Fig. 9
Fig. 9

Oscilloscope trace of the rf mixer IF output during a diode laser single-mode sweep through three NH3 absorption lines in the 965-cm−1 region.

Fig. 10
Fig. 10

Comparison of (a) direct absorption, (b) single-tone, and (c) two-tone spectra of NH3 lines using a lead-salt laser operating near 1620 cm−1.

Equations (29)

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E 1 ( t ) = E 0 ( t ) n = r n exp ( i 2 π n ν t ) ,
r n ( β , M , ψ ) = k = 1 1 a k J n k ( β ) ,
E 2 ( t ) = E 0 ( t ) n , m r n r m exp [ i 2 π ( n ν 1 + m ν 2 ) t ] .
I Ω ( t ) = c 8 π | E 0 ( t ) | 2 2 cos ( 2 π Ω t ) n , m r n r m r n 1 * r m + 1 * × exp [ 2 α ( ν 0 + ( n + m ) ν m ) ] c 8 π | E 0 ( t ) | 2 2 cos ( 2 π Ω t ) [ Q ( α ) + M 2 ] .
I Ω ( t ) = c 8 π | E 0 ( t ) | 2 2 M 2 cos ( 2 π Ω t ) .
I Ω ( t ) = c 8 π | E 0 ( t ) | 2 cos ( 2 π Ω t ) [ 2 M 2 + 2 α 0 ( β 2 M 2 ) α + ( β 2 + 2 M β sin ψ + M 2 ) α ( β 2 2 M β sin ψ + M 2 ) ] ,
SNR = CNR 1 + CNR / SBR ,
CNR = CNR 0 | Q ( α ) | 2 ,
CNR 0 ( e η h ν 0 ) 2 2 P 0 2 2 e Δ f [ ( e η h ν 0 ) P 0 ( 1 + M 2 2 ) 2 + 2 k T N e R L ] , Q ( α ) n , m r n r m r n 1 * r m + 1 * exp [ 2 α ( ν 0 + ( n + m ) ν m ) ] M 2 .
SBR = SBR 0 | Q ( α ) | 2 ,
SBR 0 = P 0 2 σ P 0 2 M 4 .
α min = 1 2 n J n 2 J n 1 2 ( 1 CNR 0 + 1 SBR 0 ) 1 / 2 .
n J n 2 J n 1 2 = 0.23807 .
I ν ( t ) = c 8 π | E 0 ( t ) | 2 exp ( i 2 π ν t ) n r n r n 1 * × exp { α ( ν 0 + n ν ) α [ ν 0 + ( n 1 ) ν ] i ϕ ( ν 0 + n ν ) + i ϕ [ ν 0 + ( n 1 ) ν ] } + complex conjugate .
I ν ( t ) = c 8 π | E 0 ( t ) | 2 [ Z exp ( i 2 π ν t ) + Z * exp ( i 2 π ν t ) ] ,
Z n r n r n 1 * exp { α ( ν 0 + n ν ) α [ ν 0 + ( n 1 ) ν ] i ϕ ( ν 0 + n ν ) + i ϕ ( ν 0 + ( n 1 ) ν ) } .
I ν ( t ) = c 8 π | E 0 ( t ) | 2 ( S sin 2 π ν t + C cos 2 π ν t ) ,
S = 2 Im [ Z ] C = 2 Re [ Z ] .
Z = n r n r n 1 * = i M exp ( i ψ ) ,
I ν ( t ) = c 8 π | E 0 ( t ) | 2 2 M ( sin ψ cos 2 π ν t + cos ψ sin 2 π ν t ) .
C = β ( α α + ) + M ( 2 2 α 0 α + α ) sin ψ + M ( ϕ ϕ + ) cos ψ ,
S = β ( ϕ + ϕ + 2 ϕ 0 ) + M ( 2 2 α 0 α + α ) cos ψ M ( ϕ ϕ + ) sin ψ ,
R ( α , ϕ ) C cos ψ S sin ψ ,
SNR = ¼ CNR 0 | R ( α , ϕ ) | 2 ,
R | α , ϕ = 0 = 2 M [ sin ( ψ + δ ψ ) cos ψ cos ( ψ + δ ψ ) sin ψ ] = 2 M sin ( δ ψ ) .
SBR = P 0 2 4 M 2 sin 2 δ ψ σ P 0 2 | R ( α , ϕ ) | 2 ¼ SBR 0 | R ( α , ϕ ) | 2 .
| R ( α , ϕ ) | min = 2 [ 1 CNR 0 + 1 SBR 0 ] 1 / 2 .
Z J 0 ( β ) J 1 ( β ) [ ( α α + ) + i ( 2 ϕ 0 ϕ + ϕ ) ] , R 2 J 0 ( β ) J 1 ( β ) [ ( α α + ) cos ψ + ( 2 ϕ 0 ϕ + ϕ ) sin ψ ] .
s min [ ( Δ α ) cos ψ + ( Δ 2 ϕ ) sin ψ ] | min 1 J 0 ( β ) J 1 ( β ) ( 1 CNR 0 + 1 SBR 0 ) 1 / 2 ,

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