Abstract

An analysis of the harmonic content in frequency-modulation and wavelength-modulation spectroscopy with a semiconductor diode laser under injection-current modulation is presented. It is argued that it is the optical power rather than the electric field that is directly modulated by the injection current. A description that is valid for both frequency-modulation and wavelength-modulation spectroscopy based on this concept is developed, and special attention is given to the residual amplitude modulation and second-harmonic (2 f) detection. Data obtained by measuring the magnitudes of the first and second harmonic of the modulation frequency of the output of a 1.31-µm distributed-feedback diode laser under sinusoidal modulation of the current and the 2 f absorption spectrum of water vapor in wavelength-modulation spectroscopy are presented. These data support the concept that it is the optical power of a diode laser that is directly modulated by modulation of the injection current.

© 1997 Optical Society of America

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References

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1995

1994

J. M. Supplee, E. A. Whittaker, and W. Lenth, “Theoretical description of frequency modulation and wavelength modulation spectroscopy,” Appl. Opt. 33, 6294–6302 (1994).
[CrossRef] [PubMed]

P. Kauranen and V. G. Avetisov, “Determination of absorption line parameters using two-tone frequency-modulation spectroscopy with diode lasers,” Opt. Commun. 106, 213–217 (1994).
[CrossRef]

1993

1992

1991

P. S. Lee, R. F. Majkowski, and T. A. Perry, “Tunable diode laser spectroscopy for isotope analysis-detection of isotopic carbon monoxide in exhaled breath,” IEEE Trans. Biomed. Eng. 38, 966–972 (1991).
[CrossRef] [PubMed]

1989

1988

1987

1986

1985

1984

W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. 20, 1045–1050 (1984).
[CrossRef]

1983

P. Pokrowsky, W. Zapka, F. Chu, and G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983).
[CrossRef]

W. Lenth, “Optical heterodyne spectroscopy with frequency- and amplitude-modulated semiconductor lasers,” Opt. Lett. 8, 575–577 (1983).
[CrossRef] [PubMed]

1982

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers: two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
[CrossRef]

1981

J. Reid and D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

1980

1977

1970

Adler-Golden, S. M.

Anderson, R. C.

Avetisov, V. G.

P. Kauranen and V. G. Avetisov, “Determination of absorption line parameters using two-tone frequency-modulation spectroscopy with diode lasers,” Opt. Commun. 106, 213–217 (1994).
[CrossRef]

Barbe, A.

Bjorklund, G. C.

Bomse, D. S.

Brown, L. R.

Camy-Peyret, C.

Carlisle, C. B.

Cassidy, D. T.

Chu, F.

P. Pokrowsky, W. Zapka, F. Chu, and G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983).
[CrossRef]

Cooper, D. E.

Flaud, J.-M.

Gallagher, T. F.

Gamache, R. R.

Gehrtz, M.

Goldman, A.

Goldstein, N.

Hager , Jr., R. N.

Hall, J. L.

Husson, N.

Janik, G. R.

Kauranen, P.

P. Kauranen and V. G. Avetisov, “Determination of absorption line parameters using two-tone frequency-modulation spectroscopy with diode lasers,” Opt. Commun. 106, 213–217 (1994).
[CrossRef]

Labrie, D.

J. Reid and D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Lee, P. S.

P. S. Lee, R. F. Majkowski, and T. A. Perry, “Tunable diode laser spectroscopy for isotope analysis-detection of isotopic carbon monoxide in exhaled breath,” IEEE Trans. Biomed. Eng. 38, 966–972 (1991).
[CrossRef] [PubMed]

Lenth, W.

Majkowski, R. F.

P. S. Lee, R. F. Majkowski, and T. A. Perry, “Tunable diode laser spectroscopy for isotope analysis-detection of isotopic carbon monoxide in exhaled breath,” IEEE Trans. Biomed. Eng. 38, 966–972 (1991).
[CrossRef] [PubMed]

Moses, E. I.

Perry, T. A.

P. S. Lee, R. F. Majkowski, and T. A. Perry, “Tunable diode laser spectroscopy for isotope analysis-detection of isotopic carbon monoxide in exhaled breath,” IEEE Trans. Biomed. Eng. 38, 966–972 (1991).
[CrossRef] [PubMed]

Pickett, H. M.

Pokrowsky, P.

P. Pokrowsky, W. Zapka, F. Chu, and G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983).
[CrossRef]

Poynter, R. L.

Reid, J.

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers: two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
[CrossRef]

J. Reid and D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Rinsland, C. P.

Rothman, L. S.

Silver, J. A.

Smith, M. A. H.

Stanton, A. C.

Supplee, J. M.

Tang, C. L.

Toth, R. A.

Warren, R. E.

Whittaker, E. A.

Wong, N. C.

Zapka, W.

P. Pokrowsky, W. Zapka, F. Chu, and G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983).
[CrossRef]

Zhu, X.

Appl. Opt.

D. E. Cooper and R. E. Warren, “Frequency modulation spectroscopy with lead-salt diode lasers: a comparison of single-tone and two-tone techniques,” Appl. Opt. 26, 3726–3732 (1987).
[CrossRef] [PubMed]

L. S. Rothman, R. R. Gamache, A. Goldman, L. R. Brown, R. A. Toth, H. M. Pickett, R. L. Poynter, J.-M. Flaud, C. Camy-Peyret, A. Barbe, N. Husson, C. P. Rinsland, and M. A. H. Smith, “The HITRAN database: 1986 edition,” Appl. Opt. 26, 4058–4097 (1987).
[CrossRef] [PubMed]

D. T. Cassidy, “Trace gas detection using 1.3-μm InGaAsP diode laser transmitter modules,” Appl. Opt. 27, 610–614 (1988).
[CrossRef] [PubMed]

J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,” Appl. Opt. 31, 707–717 (1992).
[CrossRef] [PubMed]

D. S. Bomse, A. C. Stanton, and J. A. Silver, “Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser,” Appl. Opt. 31, 718–731 (1992).
[CrossRef] [PubMed]

N. Goldstein and S. M. Adler-Golden, “Long-atmospheric-path measurements of near-visible absorption lines of O2 isotopes and H2O with a prototype AlGaAs laser transceiver system,” Appl. Opt. 32, 5849–5855 (1993).
[CrossRef] [PubMed]

J. M. Supplee, E. A. Whittaker, and W. Lenth, “Theoretical description of frequency modulation and wavelength modulation spectroscopy,” Appl. Opt. 33, 6294–6302 (1994).
[CrossRef] [PubMed]

X. Zhu and D. T. Cassidy, “Electronic subtracter for trace-gas detection with InGaAsP diode lasers,” Appl. Opt. 34, 8303–8308 (1995).
[CrossRef] [PubMed]

Appl. Phys. B

J. Reid and D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers: two-tone modulation,” Appl. Phys. B 29, 279–285 (1982).
[CrossRef]

IEEE J. Quantum Electron.

W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. 20, 1045–1050 (1984).
[CrossRef]

IEEE Trans. Biomed. Eng.

P. S. Lee, R. F. Majkowski, and T. A. Perry, “Tunable diode laser spectroscopy for isotope analysis-detection of isotopic carbon monoxide in exhaled breath,” IEEE Trans. Biomed. Eng. 38, 966–972 (1991).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Commun.

P. Kauranen and V. G. Avetisov, “Determination of absorption line parameters using two-tone frequency-modulation spectroscopy with diode lasers,” Opt. Commun. 106, 213–217 (1994).
[CrossRef]

P. Pokrowsky, W. Zapka, F. Chu, and G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983).
[CrossRef]

Opt. Lett.

Other

A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991), Chap. 11.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), p. 980.

R. N. Bracewell, The Fourier Transform and Its Application, 2nd ed., revised (McGraw-Hill, New York, 1986), p. 4.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1966), p. 151.

L. Rode and B. Westergren, Beta Mathematics Handbook, 2nd ed. (CRC Press, Boca Raton, Fla., 1992).

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Figures (3)

Fig. 1
Fig. 1

(a) Optical power versus current curve (L–I curve) for a DFB laser. (b) Output of the detector as observed on a digital oscilloscope for modulation of the current to the DFB laser. (c) Modulation of the current of the DFB as observed on a digital oscilloscope. The current modulation and concomitant optical power modulation are shown schematically in (a).

Fig. 2
Fig. 2

Magnitudes of the first harmonic (1f) and second harmonic (2 f) and the ratio of the magnitude of the 2 f to the 1f signals as a function of the modulation index M. The 2 f/1f ratio predicted under the assumption that it is the electric field that is directly modulated by modulation of the injection current is shown.

Fig. 3
Fig. 3

(a) Measured second-harmonic (2 f) signal for transmission through 18 m of water at 200 Torr. Note the essentially zero background signal (RAM signal) and the second-derivative line shape. (b) Predicted 2 f signal.

Equations (29)

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E(t)=E01+M sin(ωmt+ψ)×exp(iω0t+iβ sin ωmt)=E0 exp(iω0t)1+M sin(ωmt+ψ)× n=-Jn(β)exp(inωmt),
E(t)=E0 exp(iω0t)n=-rn exp(inωmt),
rn=k=-akJn-k(β)
a0=1-j=1 1×3×5(4j-3)24jj!j!M2j,
ak=-ik exp(ikψ)×j=1 1×3×5(4j+2|k|+-7)24j+2|k|-4(j+|k|-1)!(j-1)!×M2j+|k|-2,
ET(t)=E0 exp(iω0t)n=-T(ωn)rn exp(inωmt)
IT(t)=c8πE02n=-n=-T(ωn)T*(ωn)rnrn*×exp[i(n-n)ωmt].
IT(t)=I0 exp(iqωmt)n=-rn+qrn*×exp(-δn+q-iϕn+q-δn+iϕn)+c.c.
n=-Jn-k(β)Jn-k(β)=J-k+k(0)=δkk
IRAMI0=1n=0M sin(ωmt+ψ)n=10n2.
I2 f=2J1(β)J-1(β)exp(-2δ0)×exp(-δ1-δ-1+2δ0)cos(2ωmt-ϕ1+ϕ-1)+2 exp(-2δ0)n=0Jn(β)Jn+2(β)×[exp(-δn-δn+2+2δ0)×cos(2ωmt-ϕn+2+ϕn)+exp(-δ-n-δ-n-2+2δ0)×cos(2ωmt+ϕ-n-2-ϕ-n).
I2 f=2J1(β)J-1(β)exp(-2δ0)[2Δϕ sin(2ωmt)+(1-Δ2δ-2Δ2ϕ)cos(2ωmt)]+2 exp(-2δ0)n=0Jn(β)Jn+2(β)×[2+2n(n+2)Δ2δ-4Δ2ϕ]cos(2ωmt)+8Δϕ exp(-2δ0)n=0Jn(β)Jn+2(β)sin(2ωmt).
J1(β)J-1(β)+2n=0Jn(β)Jn+2(β)=0,
I2 f=4 exp(-2δ0)Δ2δ cos(2ωmt)×n=0(n+1)2Jn(β)Jn+2(β).
I2 f=Δδ2β22=Δδ2β2ωm22=12d2δdω2(βωm)2.
(1+x)1/2=1+12x+n=1×1×3×5(2n-1)2n+1(n+1)!(-1)nxn+1,
sin2n-1 x=(-1)n-122n-2p=0n-1 (2n-1)!(-1)p(2n-p-1)!p!×sin(2n-2p-1)x,
sin2n x=(-1)n22n-1p=0n-1 (2n)!(-1)p(2n-p)!p!×cos(2n-2p)x+(2n)!22nn!n!.
a0=1-M216-15M41024,
a1=-iM4+3M3128exp(iψ),
a-1=iM4+3M3128exp(-iψ),
a2=M232+5M4512exp(i2ψ),
a-2=M232+5M4512exp(-i2ψ),
a3=i M3128exp(i3ψ),a-3=-i M3128exp(-i3ψ),
a4=-5M42048exp(i4ψ),a-4=-5M42048exp(-i4ψ).
E(t)=E0[1+M sin(ωmt+ψ)]exp(iω0t+iβ sin ωmt)=E0 exp(iω0t)[1+M sin(ωmt+ψ)]×n=-Jn(β)exp(inωmt)
E(t)=E0 exp(iω0t)n=-rn exp(inωmt),
rn=k=-11akJn-k(β),a0=1,a±1=±M2iexp(±iψ).
IRAMI0=1+M2/2n=02M sin(ωmt+ψ)n=1-M2/2 cos[2(ωmt+ψ)]n=20n3.

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