Abstract

Recently a technique to optically eliminate the background residual amplitude modulation in 1f wavelength modulation spectroscopy was demonstrated, where perfect elimination throughout the scan range was not achieved due to the wavelength-dependence of couplers and that of the laser intensity modulation. This paper theoretically analyzes the technique and experimentally demonstrates that the elimination can be perfect for one of three possible experimental configurations, making this important for potential applications with some recently-developed laser sources. For the other configurations a non-zero background slope is predicted, experimentally verified, and the anomalous nature of signals is thereby explained. A common signal normalization method is devised that is independent of the signal slope, a fact that is important for industrial deployment of such systems.

© 2009 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  18. C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
    [CrossRef]
  19. M. J. F. Digonnet and H. J. Shaw, “Analysis of a tunable single-mode optical fiber coupler,” IEEE J. Quant Elec. 18(4), 746–754 (1982).
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  20. T. Findakly and C. Chen, “Optical directional couplers with variable spacing,” Appl. Opt. 17(5), 769–773 (1978).
    [CrossRef] [PubMed]
  21. R. Tewari and K. Thyagarajan, “Analysis of tunable single-mode fiber directional couplers using simple and accurate relations,” J. Lightwave Technol. 4(4), 386–390 (1986).
    [CrossRef]
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2009 (1)

2008 (3)

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

A. Hangauer, J. Chen, R. Strzoda, M. Ortsiefer, and M.-C. Amann, “Wavelength modulation spectroscopy with a widely tunable InP-based 2.3 microm vertical-cavity surface-emitting laser,” Opt. Lett. 33(14), 1566–1568 (2008).
[CrossRef] [PubMed]

2007 (1)

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

2006 (1)

2005 (1)

J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
[CrossRef]

2004 (2)

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Large-modulation-depth 2f spectroscopy with diode lasers for rapid temperature and species measurements in gases with blended and broadened spectra,” Appl. Opt. 43(35), 6500–6509 (2004).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

1998 (2)

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

1997 (1)

1993 (1)

1986 (1)

R. Tewari and K. Thyagarajan, “Analysis of tunable single-mode fiber directional couplers using simple and accurate relations,” J. Lightwave Technol. 4(4), 386–390 (1986).
[CrossRef]

1985 (1)

K. Thyagarajan and R. Tewari, “Accurate analysis of single-mode graded-index fiber directional couplers,” J. Lightwave Technol. 3(1), 59–62 (1985).
[CrossRef]

1982 (2)

D. T. Cassidy and J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21(7), 1185–1190 (1982).
[CrossRef] [PubMed]

M. J. F. Digonnet and H. J. Shaw, “Analysis of a tunable single-mode optical fiber coupler,” IEEE J. Quant Elec. 18(4), 746–754 (1982).
[CrossRef]

1981 (1)

J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers – comparisons of experiment and theory,” Appl. Phys. B 26(3), 203–210 (1981).
[CrossRef]

1978 (2)

Amann, M. C.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Amann, M.-C.

Axner, O.

Ballik, E. A.

Bohm, G.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Cassidy, D. T.

Chakraborty, A. L.

Chen, C.

Chen, J.

Culshaw, B.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

Debernardi, P.

J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
[CrossRef]

Digonnet, M. J. F.

M. J. F. Digonnet and H. J. Shaw, “Analysis of a tunable single-mode optical fiber coupler,” IEEE J. Quant Elec. 18(4), 746–754 (1982).
[CrossRef]

Dong, F.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

Duffin, K.

A. L. Chakraborty, K. Ruxton, W. Johnstone, M. Lengden, and K. Duffin, “Elimination of residual amplitude modulation in tunable diode laser wavelength modulation spectroscopy using an optical fiber delay line,” Opt. Express 17(12), 9602–9607 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-12-9602 .
[CrossRef] [PubMed]

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

Findakly, T.

Fujisawa, T.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Garside, B. K.

Hangauer, A.

Hanson, R. K.

Jeffries, J. B.

Johnstone, W.

A. L. Chakraborty, K. Ruxton, W. Johnstone, M. Lengden, and K. Duffin, “Elimination of residual amplitude modulation in tunable diode laser wavelength modulation spectroscopy using an optical fiber delay line,” Opt. Express 17(12), 9602–9607 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-12-9602 .
[CrossRef] [PubMed]

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

Kano, F.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Kasaya, K.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Kluczynski, P.

Kohleer, F.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Kondo, Y.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Labrie, D.

J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers – comparisons of experiment and theory,” Appl. Phys. B 26(3), 203–210 (1981).
[CrossRef]

Lauer, C.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Lengden, M.

Li, H.

Liu, J. T. C.

Liu, X.

McGettrick, A. J.

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

Michalzik, R.

J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
[CrossRef]

Mitsuhara, M.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Moodie, D.

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

Moodie, D. G.

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

Morante, M. A.

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

Nunoya, N.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Orstiefer, M.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Ortsiefer, M.

Ostermann, J. M.

J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
[CrossRef]

Philippe, L. C.

Reid, J.

Rieker, G. B.

Rinaldi, F.

J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
[CrossRef]

Robert, P.

Ronneberg, E.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Rosskopf, J.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Ruxton, K.

Sato, T.

T. Sato, M. Mitsuhara, N. Nunoya, T. Fujisawa, K. Kasaya, F. Kano, and Y. Kondo, “2.33μm wavelength distributed feedback lasers with InAs-In0.53Ga0.47As multiple quantum wells on InP substrates,” IEEE Photon. Technol. Lett. 20(12), 1045–1047 (2008).
[CrossRef]

Schilt, S.

Shau, R.

C. Lauer, M. Orstiefer, R. Shau, J. Rosskopf, G. Bohm, E. Ronneberg, F. Kohleer, and M. C. Amann, “80°C continuous-wave operation of 2.01μm wavelength InGaAlAs-InP vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 16, 2209–2211 (2004).
[CrossRef]

Shaw, H. J.

M. J. F. Digonnet and H. J. Shaw, “Analysis of a tunable single-mode optical fiber coupler,” IEEE J. Quant Elec. 18(4), 746–754 (1982).
[CrossRef]

Shewchun, J.

Stewart, G.

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

Strzoda, R.

Tandy, C.

G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
[CrossRef]

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
[CrossRef]

Tewari, R.

R. Tewari and K. Thyagarajan, “Analysis of tunable single-mode fiber directional couplers using simple and accurate relations,” J. Lightwave Technol. 4(4), 386–390 (1986).
[CrossRef]

K. Thyagarajan and R. Tewari, “Accurate analysis of single-mode graded-index fiber directional couplers,” J. Lightwave Technol. 3(1), 59–62 (1985).
[CrossRef]

Thévenaz, L.

Thyagarajan, K.

R. Tewari and K. Thyagarajan, “Analysis of tunable single-mode fiber directional couplers using simple and accurate relations,” J. Lightwave Technol. 4(4), 386–390 (1986).
[CrossRef]

K. Thyagarajan and R. Tewari, “Accurate analysis of single-mode graded-index fiber directional couplers,” J. Lightwave Technol. 3(1), 59–62 (1985).
[CrossRef]

Zhu, X.

Appl. Opt. (8)

J. Reid, J. Shewchun, B. K. Garside, and E. A. Ballik, “High sensitivity pollution detection employing tunable diode lasers,” Appl. Opt. 17(2), 300–307 (1978).
[CrossRef] [PubMed]

D. T. Cassidy and J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21(7), 1185–1190 (1982).
[CrossRef] [PubMed]

S. Schilt, L. Thévenaz, and P. Robert, “Wavelength modulation spectroscopy: combined frequency and intensity laser modulation,” Appl. Opt. 42(33), 6728–6738 (2003).
[CrossRef] [PubMed]

L. C. Philippe and R. K. Hanson, “Laser diode wavelength modulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows,” Appl. Opt. 32(30), 6090–6103 (1993).
[CrossRef] [PubMed]

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Large-modulation-depth 2f spectroscopy with diode lasers for rapid temperature and species measurements in gases with blended and broadened spectra,” Appl. Opt. 43(35), 6500–6509 (2004).
[CrossRef] [PubMed]

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

P. Kluczynski and O. Axner, “Theoretical description based on fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38(27), 5803–5815 (1999).
[CrossRef] [PubMed]

T. Findakly and C. Chen, “Optical directional couplers with variable spacing,” Appl. Opt. 17(5), 769–773 (1978).
[CrossRef] [PubMed]

Appl. Phys. B (1)

J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers – comparisons of experiment and theory,” Appl. Phys. B 26(3), 203–210 (1981).
[CrossRef]

IEEE J. Lightwave Technol. (2)

K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a calibration-free approach to the recovery of absolute gas absorption line shapes,” IEEE J. Lightwave Technol. 25(10), 3114–3125 (2007).
[CrossRef]

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: a phasor decomposition method for calibration-fee measurements of gas concentration and pressure,” IEEE J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

IEEE J. Quant Elec. (1)

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J. M. Ostermann, F. Rinaldi, P. Debernardi, and R. Michalzik, “VCSELs with enhanced single-mode power and stabilized polarization for oxygen sensing,” IEEE Photon. Technol. Lett. 17(11), 2256–2258 (2005).
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J. Opt. Soc. Am. B (1)

Opt. Express (1)

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Sens. Actuators B Chem. (2)

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection–from concept to system realisation,” Sens. Actuators B Chem. 51(1-3), 25–37 (1998).
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G. Stewart, C. Tandy, D. Moodie, M. A. Morante, and F. Dong, “Design of a fibre optic multi–point sensor for gas detection,” Sens. Actuators B Chem. 51(1-3), 227–232 (1998).
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Other (3)

A. Ghatak, and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University Press, 1999), Chap. 17.

A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997), Chap. 13.

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Figures (9)

Fig. 1
Fig. 1

RAM nulled gas absorption signals recovered by the lock-in amplifier.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Variation of (a) Intensity and (b) ∆I(λ) of the DFB, and the 3-dB coupler’s fractional coupling ratios (c) y2 (λ) and (d) y1 (λ)

Fig. 4
Fig. 4

Simulation and experiments for configuration 1 - DFB connected to IP2 of coupler1; output from OP1 of coupler2. Concentration 1.02%, pressure 1.038 bar and temperature 19.2°C.

Fig. 5
Fig. 5

Simulation and experiments for configuration 2 - DFB connected to IP2 of coupler1; output from OP2 of coupler2. Concentration 0.1%, pressure 1.038 bar and temperature 19.2°C.

Fig. 6
Fig. 6

Simulation and experiments for configuration 3 - DFB connected to IP1 of coupler1; output from OP1 of coupler2. Concentration 1.02%, pressure 1.038 bar and temperature 19.2°C.

Fig. 7
Fig. 7

Simulated variation of (a) intensity vs current, (b) ΔI(λ) vs λ for a laser with highly nonlinear laser characteristics

Fig. 8
Fig. 8

Simulated output for the perfectly nulled case for the three configurations for highly nonlinear laser characteristics

Fig. 9
Fig. 9

Experimental results: methane concentration 0.1017%, pressure 1.082 bar and temperature 20.6°C.

Equations (24)

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I P 2 = α L y 10 Δ I ( λ 0 ) cos ω t
I P 1 = x α L y 20 Δ I ( λ 0 ) cos ( ω t + π ) = x α L y 20 Δ I ( λ 0 ) cos ω t
O P 1 n o g a s = ( 1 x ) α L y 10 y 20 Δ I ( λ 0 ) cos ω t
x = 1
O P 1    n o g a s = ( 1 x ) α L y 1 ( λ ) y 2 ( λ ) Δ I ( λ ) cos ω t
O P 1 g a s = [ e α ( λ ) C l x ] α L y 1 ( λ ) y 2 ( λ ) Δ I ( λ ) cos ω t
e α ( λ ) C l = 1 + O P 1 g a s O P 1 n o g a s α L y 1 ( λ ) y 2 ( λ ) Δ I ( λ ) cos ω t
O P 1    g a s = [ e α ( λ ) C l 1 ] α L y 1 ( λ ) y 2 ( λ ) Δ I ( λ ) cos ω t
e α ( λ ) C l = 1 + O P 1 g a s α L y 1 ( λ ) y 2 ( λ ) Δ I ( λ ) cos ω t
O P 2    n o g a s = ( y 10 2 x y 20 2 ) α L Δ I ( λ 0 ) cos ω t
x = ( y 10 / y 20 ) 2
O P 2    n o g a s = [ y 1 2 ( λ ) x y 2 2 ( λ ) ]    α L Δ I ( λ ) cos ω t
O P 2 g a s = [ y 1 2 ( λ ) e α ( λ ) C l x y 2 2 ( λ ) ] α L Δ I ( λ ) cos ω t
e α ( λ ) C l = 1 + O P 2 g a s O P 2 n o g a s α L y 1 2 ( λ ) Δ I ( λ ) cos ω t
I P 2 = α L y 20 Δ I ( λ 0 ) cos ω t
I P 1 = x α L y 10 Δ I ( λ 0 ) cos ω t
O P 1 n o g a s = ( y 20 2 x y 10 2 ) α L Δ I ( λ 0 ) cos ω t
x = ( y 20 / y 10 ) 2
O P 1    n o g a s = [ y 2 2 ( λ ) x y 1 2 ( λ ) ] α L Δ I ( λ ) cos ω t
O P 1 g a s = [ y 2 2 ( λ ) e α ( λ ) C l x y 1 2 ( λ ) ] α L Δ I ( λ ) cos ω t
e α ( λ ) C l = 1 + O P 1 g a s O P 1 n o g a s α L y 2 2 ( λ ) Δ I ( λ ) cos ω t
y 1 ( λ ) = cos 2 [ κ ( λ ) L c / 2 ]
y 2 ( λ ) = sin 2 [ κ ( λ ) L c / 2 ]
κ ( λ ) = π 2 δ a e ( A + B d 1 + C d 1 2 )

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