Abstract

Doppler broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry (Db-NICE-OHMS) has been scrutinized with respect to modulation and demodulation conditions (encompassing the modulation frequency, νm, the modulation index, β, and the detection phase, θ), the cavity length, L, and the modulation order, k (defined as νm/νFSR, where νFSR is the free-spectral range of the cavity), primarily in the Doppler limit but also for two specific situations in the Voigt regime (for equal Doppler and homogeneous width and for purely Lorentzian broadened transitions), both in the absence and presence of optical saturation (the latter for the case in which the homogeneous broadening is smaller than the modulation frequency). It is found that, for a system with a given cavity length, the optimum conditions (i.e., those that produce the largest NICE-OHMS signal) for an unsaturated transition in the Doppler limit comprise νm/ΓD=1.6 (where ΓD is the half-width at half-maximum of the Doppler width of the transition), β=1.3, and θ=0.78π. It is also found that the maximum is rather broad; the signal takes 95% of its maximum value for modulation frequencies in the entire 0.4νm/ΓD2.4 range. When optical saturation sets in, θ shifts toward the dispersion phase. The optimum conditions encompass k>1 whenever L>0.35LD and 2.6LD for the dispersion and absorption modes of detection, respectively [where LD is a characteristic length given by c/(2ΓD)]. Similar conditions are found under pressure broadened conditions.

© 2014 Optical Society of America

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  1. A. Foltynowicz, F. M. Schmidt, W. Ma, and O. Axner, “Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: current status and future potential,” Appl. Phys. B 92, 313–326 (2008).
    [CrossRef]
  2. J. Ye, L. Ma, and J. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am. B 15, 6–15 (1998).
    [CrossRef]
  3. L. Ma, J. Ye, P. Dube, and J. Hall, “Ultrasensitive frequency-modulation spectroscopy enhanced by a high-finesse optical cavity: theory and application to overtone transitions of C2H2 and C2HD,” J. Opt. Soc. Am. B 16, 2255–2268 (1999).
    [CrossRef]
  4. C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66  μm tunable diode laser,” Jpn. J. Appl. Phys. 38, 920–922 (1999).
    [CrossRef]
  5. C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65  μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
    [CrossRef]
  6. L. Gianfrani, R. Fox, and L. Hollberg, “Cavity-enhanced absorption spectroscopy of molecular oxygen,” J. Opt. Soc. Am. B 16, 2247–2254 (1999).
    [CrossRef]
  7. M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).
  8. N. van Leeuwen and A. Wilson, “Measurement of pressure-broadened, ultraweak transitions with noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 21, 1713–1721 (2004).
    [CrossRef]
  9. N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
    [CrossRef]
  10. J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
    [CrossRef]
  11. C. L. Bell, G. Hancock, R. Peverall, G. A. D. Ritchie, J. H. van Helden, and N. J. van Leeuwen, “Characterization of an external cavity diode laser based ring cavity NICE-OHMS system,” Opt. Express 17, 9834–9839 (2009).
    [CrossRef]
  12. M. W. Porambo, B. M. Siller, J. M. Pearson, and B. J. McCall, “Broadly tunable mid-infrared noise-immune cavity-enhanced optical heterodyne molecular spectrometer,” Opt. Lett. 37, 4422–4424 (2012).
    [CrossRef]
  13. F. M. Schmidt, A. Foltynowicz, W. Ma, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry for Doppler-broadened detection of C2H2 in the parts per trillion range,” J. Opt. Soc. Am. B 24, 1392–1405 (2007).
    [CrossRef]
  14. P. Ehlers, I. Silander, J. Wang, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry instrumentation for Doppler-broadened detection in the 10–12cm–1Hz–1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).
    [CrossRef]
  15. P. Ehlers, J. Wang, I. Silander, and O. Axner, “Doppler broadened NICE-OHMS beyond the triplet formalism: assessment of optimum modulation index,” J. Opt. Soc. Am. B 31, 1499–1507 (2014).
    [CrossRef]
  16. W. Ma, A. Foltynowicz, and O. Axner, “Theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy under optically saturated conditions,” J. Opt. Soc. Am. B 25, 1144–1155 (2008).
    [CrossRef]
  17. O. Axner, P. Ehlers, A. Foltynowicz, I. S. Silander, and J. Wang, “NICE-OHMS—frequency modulation cavity-enhanced spectroscopy—principles and performance,” in Cavity-Enhanced Spectroscopy and Sensing, Vol. 179 of Springer Series in Optical Sciences (Springer, 2014), Chap. 6, pp. 211–251.
  18. N. Nayak and G. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985).
    [CrossRef]
  19. 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]
  20. A. Foltynowicz, W. Ma, F. M. Schmidt, and O. Axner, “Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry signals from optically saturated transitions under low pressure conditions,” J. Opt. Soc. Am. B 25, 1156–1165 (2008).
    [CrossRef]
  21. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15–17 (1980).
    [CrossRef]
  22. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
    [CrossRef]
  23. S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
    [CrossRef]
  24. A. Foltynowicz, “Fiber-laser-based NICE-OHMS,” Ph.D. thesis (Umeå University, 2009).
  25. J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width—brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
    [CrossRef]
  26. O. Axner, Department of Physics, Umeå University, Umeå, Sweden, and W. Ma are preparing a manuscript to be called “Noise-immune cavity-enhanced analytical atomic spectrometry—NICE-AAS—A technique for detection of elements down to zeptogram amounts, and zeptogram per milliliter and zeptogram per cubic centimeter concentrations.”

2014 (1)

2012 (2)

2009 (1)

2008 (3)

2007 (1)

2006 (1)

J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
[CrossRef]

2004 (3)

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

N. van Leeuwen and A. Wilson, “Measurement of pressure-broadened, ultraweak transitions with noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 21, 1713–1721 (2004).
[CrossRef]

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

2000 (1)

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65  μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef]

1999 (3)

1998 (1)

1996 (1)

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

1994 (1)

1985 (1)

N. Nayak and G. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985).
[CrossRef]

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

1980 (1)

1977 (1)

J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width—brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Agarwal, G.

N. Nayak and G. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985).
[CrossRef]

Axner, O.

P. Ehlers, J. Wang, I. Silander, and O. Axner, “Doppler broadened NICE-OHMS beyond the triplet formalism: assessment of optimum modulation index,” J. Opt. Soc. Am. B 31, 1499–1507 (2014).
[CrossRef]

P. Ehlers, I. Silander, J. Wang, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry instrumentation for Doppler-broadened detection in the 10–12cm–1Hz–1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).
[CrossRef]

W. Ma, A. Foltynowicz, and O. Axner, “Theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy under optically saturated conditions,” J. Opt. Soc. Am. B 25, 1144–1155 (2008).
[CrossRef]

A. Foltynowicz, W. Ma, F. M. Schmidt, and O. Axner, “Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry signals from optically saturated transitions under low pressure conditions,” J. Opt. Soc. Am. B 25, 1156–1165 (2008).
[CrossRef]

A. Foltynowicz, F. M. Schmidt, W. Ma, and O. Axner, “Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: current status and future potential,” Appl. Phys. B 92, 313–326 (2008).
[CrossRef]

F. M. Schmidt, A. Foltynowicz, W. Ma, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry for Doppler-broadened detection of C2H2 in the parts per trillion range,” J. Opt. Soc. Am. B 24, 1392–1405 (2007).
[CrossRef]

O. Axner, P. Ehlers, A. Foltynowicz, I. S. Silander, and J. Wang, “NICE-OHMS—frequency modulation cavity-enhanced spectroscopy—principles and performance,” in Cavity-Enhanced Spectroscopy and Sensing, Vol. 179 of Springer Series in Optical Sciences (Springer, 2014), Chap. 6, pp. 211–251.

O. Axner, Department of Physics, Umeå University, Umeå, Sweden, and W. Ma are preparing a manuscript to be called “Noise-immune cavity-enhanced analytical atomic spectrometry—NICE-AAS—A technique for detection of elements down to zeptogram amounts, and zeptogram per milliliter and zeptogram per cubic centimeter concentrations.”

Bell, C. L.

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15–17 (1980).
[CrossRef]

Bood, J.

J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
[CrossRef]

Cannon, B.

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

Dube, P.

Ehlers, P.

Fei, R.

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Foltynowicz, A.

W. Ma, A. Foltynowicz, and O. Axner, “Theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy under optically saturated conditions,” J. Opt. Soc. Am. B 25, 1144–1155 (2008).
[CrossRef]

A. Foltynowicz, W. Ma, F. M. Schmidt, and O. Axner, “Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry signals from optically saturated transitions under low pressure conditions,” J. Opt. Soc. Am. B 25, 1156–1165 (2008).
[CrossRef]

A. Foltynowicz, F. M. Schmidt, W. Ma, and O. Axner, “Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: current status and future potential,” Appl. Phys. B 92, 313–326 (2008).
[CrossRef]

F. M. Schmidt, A. Foltynowicz, W. Ma, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry for Doppler-broadened detection of C2H2 in the parts per trillion range,” J. Opt. Soc. Am. B 24, 1392–1405 (2007).
[CrossRef]

O. Axner, P. Ehlers, A. Foltynowicz, I. S. Silander, and J. Wang, “NICE-OHMS—frequency modulation cavity-enhanced spectroscopy—principles and performance,” in Cavity-Enhanced Spectroscopy and Sensing, Vol. 179 of Springer Series in Optical Sciences (Springer, 2014), Chap. 6, pp. 211–251.

A. Foltynowicz, “Fiber-laser-based NICE-OHMS,” Ph.D. thesis (Umeå University, 2009).

Fox, R.

Gianfrani, L.

Hall, G.

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Hall, J.

Hancock, G.

Hollberg, L.

Howard, D.

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

Ishibashi, C.

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65  μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef]

C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66  μm tunable diode laser,” Jpn. J. Appl. Phys. 38, 920–922 (1999).
[CrossRef]

Kjaergaard, H.

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

Lenth, W.

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]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Longbothum, R.

J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width—brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Ma, L.

Ma, W.

A. Foltynowicz, F. M. Schmidt, W. Ma, and O. Axner, “Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: current status and future potential,” Appl. Phys. B 92, 313–326 (2008).
[CrossRef]

A. Foltynowicz, W. Ma, F. M. Schmidt, and O. Axner, “Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry signals from optically saturated transitions under low pressure conditions,” J. Opt. Soc. Am. B 25, 1156–1165 (2008).
[CrossRef]

W. Ma, A. Foltynowicz, and O. Axner, “Theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy under optically saturated conditions,” J. Opt. Soc. Am. B 25, 1144–1155 (2008).
[CrossRef]

F. M. Schmidt, A. Foltynowicz, W. Ma, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry for Doppler-broadened detection of C2H2 in the parts per trillion range,” J. Opt. Soc. Am. B 24, 1392–1405 (2007).
[CrossRef]

O. Axner, Department of Physics, Umeå University, Umeå, Sweden, and W. Ma are preparing a manuscript to be called “Noise-immune cavity-enhanced analytical atomic spectrometry—NICE-AAS—A technique for detection of elements down to zeptogram amounts, and zeptogram per milliliter and zeptogram per cubic centimeter concentrations.”

McCall, B. J.

McIlroy, A.

J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
[CrossRef]

Myers, T.

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

Nayak, N.

N. Nayak and G. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985).
[CrossRef]

North, S.

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Olivero, J.

J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width—brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

Osborn, D.

J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
[CrossRef]

Pearson, J. M.

Peverall, R.

Porambo, M. W.

Ritchie, G. A. D.

Sasada, H.

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65  μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef]

C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66  μm tunable diode laser,” Jpn. J. Appl. Phys. 38, 920–922 (1999).
[CrossRef]

Schmidt, F. M.

Silander, I.

Silander, I. S.

O. Axner, P. Ehlers, A. Foltynowicz, I. S. Silander, and J. Wang, “NICE-OHMS—frequency modulation cavity-enhanced spectroscopy—principles and performance,” in Cavity-Enhanced Spectroscopy and Sensing, Vol. 179 of Springer Series in Optical Sciences (Springer, 2014), Chap. 6, pp. 211–251.

Siller, B. M.

Supplee, J. M.

Taubmann, M.

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

van Helden, J. H.

van Leeuwen, N.

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

N. van Leeuwen and A. Wilson, “Measurement of pressure-broadened, ultraweak transitions with noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 21, 1713–1721 (2004).
[CrossRef]

van Leeuwen, N. J.

Wang, J.

Whittaker, E. A.

Williams, R.

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

Wilson, A.

N. van Leeuwen and A. Wilson, “Measurement of pressure-broadened, ultraweak transitions with noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 21, 1713–1721 (2004).
[CrossRef]

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

Ye, J.

Zheng, X.

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

A. Foltynowicz, F. M. Schmidt, W. Ma, and O. Axner, “Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: current status and future potential,” Appl. Phys. B 92, 313–326 (2008).
[CrossRef]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145–152 (1983).
[CrossRef]

J. Chem. Phys. (2)

S. North, X. Zheng, R. Fei, and G. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

J. Bood, A. McIlroy, and D. Osborn, “Measurement of the sixth overtone band of nitric oxide, and its dipole moment function, using cavity-enhanced frequency modulation spectroscopy,” J. Chem. Phys. 124, 084311 (2006).
[CrossRef]

J. Mol. Spectrosc. (2)

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65  μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef]

N. van Leeuwen, H. Kjaergaard, D. Howard, and A. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. 228, 83–91 (2004).
[CrossRef]

J. Opt. Soc. Am. B (9)

N. van Leeuwen and A. Wilson, “Measurement of pressure-broadened, ultraweak transitions with noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 21, 1713–1721 (2004).
[CrossRef]

L. Gianfrani, R. Fox, and L. Hollberg, “Cavity-enhanced absorption spectroscopy of molecular oxygen,” J. Opt. Soc. Am. B 16, 2247–2254 (1999).
[CrossRef]

J. Ye, L. Ma, and J. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am. B 15, 6–15 (1998).
[CrossRef]

L. Ma, J. Ye, P. Dube, and J. Hall, “Ultrasensitive frequency-modulation spectroscopy enhanced by a high-finesse optical cavity: theory and application to overtone transitions of C2H2 and C2HD,” J. Opt. Soc. Am. B 16, 2255–2268 (1999).
[CrossRef]

A. Foltynowicz, W. Ma, F. M. Schmidt, and O. Axner, “Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry signals from optically saturated transitions under low pressure conditions,” J. Opt. Soc. Am. B 25, 1156–1165 (2008).
[CrossRef]

F. M. Schmidt, A. Foltynowicz, W. Ma, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry for Doppler-broadened detection of C2H2 in the parts per trillion range,” J. Opt. Soc. Am. B 24, 1392–1405 (2007).
[CrossRef]

P. Ehlers, I. Silander, J. Wang, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry instrumentation for Doppler-broadened detection in the 10–12cm–1Hz–1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).
[CrossRef]

P. Ehlers, J. Wang, I. Silander, and O. Axner, “Doppler broadened NICE-OHMS beyond the triplet formalism: assessment of optimum modulation index,” J. Opt. Soc. Am. B 31, 1499–1507 (2014).
[CrossRef]

W. Ma, A. Foltynowicz, and O. Axner, “Theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy under optically saturated conditions,” J. Opt. Soc. Am. B 25, 1144–1155 (2008).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width—brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66  μm tunable diode laser,” Jpn. J. Appl. Phys. 38, 920–922 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

N. Nayak and G. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985).
[CrossRef]

Spectrochim. Acta A (1)

M. Taubmann, T. Myers, B. Cannon, and R. Williams, “Stabilization, injection and control of quantum cascade lasers, and their application to chemical sensing in the infrared,” Spectrochim. Acta A 60, 3457–3468 (2004).

Other (3)

O. Axner, P. Ehlers, A. Foltynowicz, I. S. Silander, and J. Wang, “NICE-OHMS—frequency modulation cavity-enhanced spectroscopy—principles and performance,” in Cavity-Enhanced Spectroscopy and Sensing, Vol. 179 of Springer Series in Optical Sciences (Springer, 2014), Chap. 6, pp. 211–251.

O. Axner, Department of Physics, Umeå University, Umeå, Sweden, and W. Ma are preparing a manuscript to be called “Noise-immune cavity-enhanced analytical atomic spectrometry—NICE-AAS—A technique for detection of elements down to zeptogram amounts, and zeptogram per milliliter and zeptogram per cubic centimeter concentrations.”

A. Foltynowicz, “Fiber-laser-based NICE-OHMS,” Ph.D. thesis (Umeå University, 2009).

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Figures (8)

Fig. 1.
Fig. 1.

pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, in the Doppler limit as a function of normalized modulation frequency, νm/ΓD, and modulation index, β, for an unsaturated transition in the Doppler limit for (a) absorption and (b) dispersion detection phases. The colored (red) lines on the rims of the data sets represent the modulation index for which χ¯NODb,pp takes its maximum value for a given normalized modulation frequency.

Fig. 2.
Fig. 2.

pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, in the Doppler limit as a function of normalized modulation frequency, νm/ΓD, evaluated for the modulation index that maximizes the line shape function, i.e., βνm/ΓDmax, which is represented by the colored (red) curves in Fig. 1, for the cases with detection at pure absorption phase (blue, solid curve), dispersion phase (red, dashed curve), and the phase that maximizes the response (θνm/ΓDmax) (black, dashed–dotted curve), respectively.

Fig. 3.
Fig. 3.

Panels (a) and (b) show contour plots of the pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, as a function of the detection phase and the modulation index for an unsaturated and a saturated case for the optimum modulation frequency (νmmax), respectively. Panel (c) illustrates the cross sections of the plot for pure absorption (blue curve) and pure dispersion phase (red curve), as well as the phases that yield the largest line shape function (black curve), which are indicated as horizontal lines in panels (a) and (b). The numbers given in the upper two panels represent the pp values the Db-NICE-OHMS signal takes on that particular contour plot. See text for details.

Fig. 4.
Fig. 4.

Dependence of the pp value of the Db-NICE-OHMS signal, represented by Lχ¯NODb,pp/LD, on the normalized cavity length, given by L/LD, in the Doppler limit. The upper and lower sets of curves (blue and red) represent the absorption and dispersion responses, respectively, whereas the four curves in each set correspond to (from bottom to top) successively increasing modulation orders (k=1, 2, 3, and 4). The inset displays an enlargement of the dispersion response for small L/LD values.

Fig. 5.
Fig. 5.

pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, in the Voigt regime (for the case with ΓL=ΓD) as a function of normalized modulation frequency, νm/ΓV, and modulation index, β, for an unsaturated transition in the Voigt regime for (a) absorption and (b) dispersion detection phases. The colored (red) lines on the rims of the data sets represent the modulation index for which χ¯NODb,pp takes its maximum value for a given normalized modulation frequency.

Fig. 6.
Fig. 6.

pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, in the Voigt regime (for case with ΓL=ΓD) as a function of normalized modulation frequency, νm/ΓV, evaluated for the modulation index that maximizes the line shape function, i.e., βνm/ΓVmax, which is represented by the colored curves in Fig. 5, for the cases with detection at pure absorption phase (blue, solid curve), dispersion phase (red, dashed curve), and the phase that maximizes the response (θνm/ΓVmax) (black, dashed–dotted curve), respectively.

Fig. 7.
Fig. 7.

pp value of the Db-NICE-OHMS line shape function, χ¯NODb,pp, in the collision broadened regime (i.e., for case with ΓLΓD) as a function of normalized modulation frequency, νm/ΓV, evaluated for the modulation index that maximizes the line shape function for the cases with detection at pure absorption phase (blue, solid curve), dispersion phase (red, dashed curve), and the phase that maximizes the response (θνm/ΓVmax) (black, dashed–dotted curve), respectively.

Fig. 8.
Fig. 8.

Dependence of the pp value of the Db-NICE-OHMS signal represented by Lχ¯NODb,pp/LV on the normalized cavity length in the Voigt regime, given by L/LV. The upper and lower sets of curves (blue and red) represent the absorption and dispersion responses, respectively, whereas the four curves in each set correspond to (from bottom to top) successively increasing modulation orders (k>1, 2, 3, and 4). The inset displays an enlargement of the dispersion response for small L/LV values.

Equations (8)

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SNODb(Δν,νm,β,θ)=S0χ¯NODb(Δν,νm,β,θ),
χ¯NODb(Δν,νm,β,θ)=1χ0({n=0NJn(β)Jn+1(β)[χn1abs(Δν,νm)+χnabs(Δν,νm)χnabs(Δν,νm)χn+1abs(Δν,νm)]}sin(θ)+{n=0NJn(β)Jn+1(β)[χn1disp(Δν,νm)χndisp(Δν,νm)χndisp(Δν,νm)+χn+1disp(Δν,νm)]}cos(θ)),
χnabs(Δν,νm)=cπΓD11+GnRe{w[xn(Δν,νm)+iyn]}
χndisp(Δν,νm)=cπΓDIm{w[xn(Δν,νm)+iyn]},
xn(Δν,νm)=(Δν+nνm)/ΓD
yn=1+Gn(ΓL/ΓD),
χ1absχ1absχ0absν·2νm=χ0absν·2kΓD·LDL
χ1disp2χ0disp+χ1disp2χ0disp2ν·νm2=2χ0disp2ν·(kΓD)2·(LDL)2.

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