Abstract

The detection sensitivity of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) is often limited by background signals that bring in drifts. A novel realization of NICE-OHMS, termed differential NICE-OHMS, that both reduces such drifts and enlarges the molecular signal is presented. It is based on simultaneous detection of NICE-OHMS signals in reflection and transmission, followed by a subtraction of the former (properly weighted) from the latter. An Allan plot analysis shows that the instrumentation could demonstrate a noise equivalent absorption per unit length (NEAL) of 4.7 × 10−14 cm−1, obtained for an integration time of 170 s.

© 2017 Optical Society of America

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References

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  1. L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy - Applications to molecular overtones as visible frequency references,” in Laser Spectroscopy XII International Conference (World Scientific, 1995), pp. 199–203.
  2. J. Ye, L. S. Ma, and J. L. Hall, “Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy,” J. Opt. Soc. Am. B 15, 6–15 (1998).
  3. 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).
  4. O. Axner, P. Ehlers, A. Foltynowicz, I. Silander, and J. Wang, “NICE-OHMS – Frequency Modulation Cavity-Enhanced Spectroscopy – Principles and Performance,” in Cavity-Enhanced Spectroscopy and Sensing, H. P. Loock and G. Gagliardi, eds. (Springer Verlag, 2014), pp. 211–251.
  5. L. S. Ma, J. Ye, P. Dube, and J. L. 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).
  6. L. Gianfrani, R. W. Fox, and L. Hollberg, “Cavity-enhanced absorption spectroscopy of molecular oxygen,” J. Opt. Soc. Am. B 16, 2247–2254 (1999).
  7. 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(12), 9834–9839 (2009).
    [PubMed]
  8. T. Hausmaninger, I. Silander, and O. Axner, “Narrowing of the linewidth of an optical parametric oscillator by an acousto-optic modulator for the realization of mid-IR noise-immune cavity-enhanced optical heterodyne molecular spectrometry down to 10−10 cm−1 Hz−1/2,” Opt. Express 23(26), 33641–33655 (2015).
    [PubMed]
  9. B. M. Siller, M. W. Porambo, A. A. Mills, and B. J. McCall, “Noise immune cavity enhanced optical heterodyne velocity modulation spectroscopy,” Opt. Express 19(24), 24822–24827 (2011).
    [PubMed]
  10. J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
    [PubMed]
  11. G. Zhao, T. Hausmaninger, W. Ma, and O. Axner, “Whispering-gallery-mode laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry,” Opt. Lett. 42(16), 3109–3112 (2017).
    [PubMed]
  12. P. Werle, “Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence,” Appl. Phys. B 102, 313–329 (2011).
  13. N. C. Wong and J. L. Hall, “Servo control of amplitude-modulation in frequency-modulation spectroscopy - demonstration of shot-noise-limited detection,” J. Opt. Soc. Am. B 2, 1527–1533 (1985).
  14. A. Foltynowicz, I. Silander, and O. Axner, “Reduction of background signals in fiber-based NICE-OHMS,” J. Opt. Soc. Am. B 28, 2797–2805 (2011).
  15. 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 10−12 cm−1 Hz-1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).
  16. P. Ehlers, A. C. Johansson, I. Silander, A. Foltynowicz, and O. Axner, “Use of etalon-immune distances to reduce the influence of background signals in frequency-modulation spectroscopy and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 31, 2938–2945 (2014).
  17. J. Ye, “Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards,” Ph.D. Thesis (University of Colorado, Boulder, Colorado, 1997).
  18. M. L. Silva, “Spectroscopic investigations of the X and à state dynamics of 13C2H2,” PhD thesis (Massachusetts Institute of Technology, Cambridge, MA, 2002).
  19. W. G. Ma, I. Silander, T. Hausmaninger, and O. Axner, “Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition - I. Theoretical description,” J. Quant. Spectrosc. Radiat. Transf. 168, 217–244 (2016).
  20. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
  21. R. G. DeVoe and R. G. Brewer, “Laser frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).
  22. A. Khodabakhsh, C. Abd Alrahman, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy,” Opt. Lett. 39(17), 5034–5037 (2014).
    [PubMed]
  23. A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection,” Appl. Phys. B 119, 87–96 (2015).
  24. P. Ehlers, I. Silander, J. Wang, and O. Axner, “Doppler broadened NICE-OHMS beyond the triplet formalism – Assessment of the optimum modulation index,” J. Opt. Soc. Am. B 31, 1499–1507 (2014).
  25. For the case when Rc is (close to) zero the reflected NICE-OHMS signal cannot be considered to be given by a product of a spectral component of the laser beam that is affected by the molecules in the cavity and a component that is unaffected of this, as is assumed when the ordinary expressions for FMS or NICE-OHMS are derived, but rather by a product of two small molecule-induced entities. However, since Rc > 0 for the case with an impendence unbalanced cavity (as is considered in this work), we still consider Eq. (9) to be valid.
  26. I. Silander, P. Ehlers, J. Wang, and O. Axner, “Frequency modulation background signals from fiber-based electro optic modulators are caused by crosstalk,” J. Opt. Soc. Am. B 29, 916–923 (2012).
  27. I. Silander, T. Hausmaninger, and O. Axner, “Model for in-coupling of etalons into signal strengths extracted from spectral line shape fitting and methodology for predicting the optimum scanning range—Demonstration of Doppler-broadened, noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy down to 9 × 10−14 cm−1,” J. Opt. Soc. Am. B 32, 2104–2114 (2015).
  28. It should be noted for the case of two different mirrors no such general parameter was found; it is however obvious that a combination of two different mirrors opens up for tailoring the system properties (i.e. the signal and power ratios) more freely.
  29. C. J. Hood, H. J. Kimble, and J. Ye, “Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,” Phys. Rev. A 64, 033804 (2001).
  30. P. Ehlers, I. Silander, J. Wang, A. Foltynowicz, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry incorporating an optical circulator,” Opt. Lett. 39(2), 279–282 (2014).
    [PubMed]
  31. This implies that l2 and t2 could be assessed to 13 and 44 ppm, respectively.
  32. P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

2017 (1)

2016 (1)

W. G. Ma, I. Silander, T. Hausmaninger, and O. Axner, “Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition - I. Theoretical description,” J. Quant. Spectrosc. Radiat. Transf. 168, 217–244 (2016).

2015 (3)

2014 (4)

2012 (2)

2011 (3)

2009 (1)

2008 (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).

2006 (1)

J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
[PubMed]

2001 (1)

C. J. Hood, H. J. Kimble, and J. Ye, “Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,” Phys. Rev. A 64, 033804 (2001).

1999 (2)

1998 (1)

1993 (1)

P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

1985 (1)

1984 (1)

R. G. DeVoe and R. G. Brewer, “Laser frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Abd Alrahman, C.

Axner, O.

G. Zhao, T. Hausmaninger, W. Ma, and O. Axner, “Whispering-gallery-mode laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry,” Opt. Lett. 42(16), 3109–3112 (2017).
[PubMed]

W. G. Ma, I. Silander, T. Hausmaninger, and O. Axner, “Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition - I. Theoretical description,” J. Quant. Spectrosc. Radiat. Transf. 168, 217–244 (2016).

T. Hausmaninger, I. Silander, and O. Axner, “Narrowing of the linewidth of an optical parametric oscillator by an acousto-optic modulator for the realization of mid-IR noise-immune cavity-enhanced optical heterodyne molecular spectrometry down to 10−10 cm−1 Hz−1/2,” Opt. Express 23(26), 33641–33655 (2015).
[PubMed]

I. Silander, T. Hausmaninger, and O. Axner, “Model for in-coupling of etalons into signal strengths extracted from spectral line shape fitting and methodology for predicting the optimum scanning range—Demonstration of Doppler-broadened, noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy down to 9 × 10−14 cm−1,” J. Opt. Soc. Am. B 32, 2104–2114 (2015).

P. Ehlers, A. C. Johansson, I. Silander, A. Foltynowicz, and O. Axner, “Use of etalon-immune distances to reduce the influence of background signals in frequency-modulation spectroscopy and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 31, 2938–2945 (2014).

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

P. Ehlers, I. Silander, J. Wang, A. Foltynowicz, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry incorporating an optical circulator,” Opt. Lett. 39(2), 279–282 (2014).
[PubMed]

I. Silander, P. Ehlers, J. Wang, and O. Axner, “Frequency modulation background signals from fiber-based electro optic modulators are caused by crosstalk,” J. Opt. Soc. Am. B 29, 916–923 (2012).

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 10−12 cm−1 Hz-1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).

A. Foltynowicz, I. Silander, and O. Axner, “Reduction of background signals in fiber-based NICE-OHMS,” J. Opt. Soc. Am. B 28, 2797–2805 (2011).

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).

Bell, C. L.

Bood, J.

J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
[PubMed]

Brewer, R. G.

R. G. DeVoe and R. G. Brewer, “Laser frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).

DeVoe, R. G.

R. G. DeVoe and R. G. Brewer, “Laser frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Dube, P.

Dubé, P.

L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy - Applications to molecular overtones as visible frequency references,” in Laser Spectroscopy XII International Conference (World Scientific, 1995), pp. 199–203.

Ehlers, P.

Foltynowicz, A.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Fox, R. W.

Gianfrani, L.

Hall, J. L.

L. S. Ma, J. Ye, P. Dube, and J. L. 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).

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

N. C. Wong and J. L. Hall, “Servo control of amplitude-modulation in frequency-modulation spectroscopy - demonstration of shot-noise-limited detection,” J. Opt. Soc. Am. B 2, 1527–1533 (1985).

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy - Applications to molecular overtones as visible frequency references,” in Laser Spectroscopy XII International Conference (World Scientific, 1995), pp. 199–203.

Hancock, G.

Hausmaninger, T.

Hollberg, L.

Hood, C. J.

C. J. Hood, H. J. Kimble, and J. Ye, “Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,” Phys. Rev. A 64, 033804 (2001).

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Johansson, A. C.

A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection,” Appl. Phys. B 119, 87–96 (2015).

P. Ehlers, A. C. Johansson, I. Silander, A. Foltynowicz, and O. Axner, “Use of etalon-immune distances to reduce the influence of background signals in frequency-modulation spectroscopy and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 31, 2938–2945 (2014).

Khodabakhsh, A.

A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection,” Appl. Phys. B 119, 87–96 (2015).

A. Khodabakhsh, C. Abd Alrahman, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy,” Opt. Lett. 39(17), 5034–5037 (2014).
[PubMed]

Kimble, H. J.

C. J. Hood, H. J. Kimble, and J. Ye, “Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,” Phys. Rev. A 64, 033804 (2001).

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Ma, L. S.

Ma, W.

G. Zhao, T. Hausmaninger, W. Ma, and O. Axner, “Whispering-gallery-mode laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry,” Opt. Lett. 42(16), 3109–3112 (2017).
[PubMed]

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).

Ma, W. G.

W. G. Ma, I. Silander, T. Hausmaninger, and O. Axner, “Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition - I. Theoretical description,” J. Quant. Spectrosc. Radiat. Transf. 168, 217–244 (2016).

McCall, B. J.

McIlroy, A.

J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
[PubMed]

Mills, A. A.

Mucke, R.

P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Osborn, D. L.

J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
[PubMed]

Peverall, R.

Porambo, M. W.

Ritchie, G. A. D.

Schmidt, F. M.

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).

Silander, I.

W. G. Ma, I. Silander, T. Hausmaninger, and O. Axner, “Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition - I. Theoretical description,” J. Quant. Spectrosc. Radiat. Transf. 168, 217–244 (2016).

I. Silander, T. Hausmaninger, and O. Axner, “Model for in-coupling of etalons into signal strengths extracted from spectral line shape fitting and methodology for predicting the optimum scanning range—Demonstration of Doppler-broadened, noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy down to 9 × 10−14 cm−1,” J. Opt. Soc. Am. B 32, 2104–2114 (2015).

T. Hausmaninger, I. Silander, and O. Axner, “Narrowing of the linewidth of an optical parametric oscillator by an acousto-optic modulator for the realization of mid-IR noise-immune cavity-enhanced optical heterodyne molecular spectrometry down to 10−10 cm−1 Hz−1/2,” Opt. Express 23(26), 33641–33655 (2015).
[PubMed]

P. Ehlers, A. C. Johansson, I. Silander, A. Foltynowicz, and O. Axner, “Use of etalon-immune distances to reduce the influence of background signals in frequency-modulation spectroscopy and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 31, 2938–2945 (2014).

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

P. Ehlers, I. Silander, J. Wang, A. Foltynowicz, and O. Axner, “Fiber-laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry incorporating an optical circulator,” Opt. Lett. 39(2), 279–282 (2014).
[PubMed]

I. Silander, P. Ehlers, J. Wang, and O. Axner, “Frequency modulation background signals from fiber-based electro optic modulators are caused by crosstalk,” J. Opt. Soc. Am. B 29, 916–923 (2012).

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 10−12 cm−1 Hz-1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).

A. Foltynowicz, I. Silander, and O. Axner, “Reduction of background signals in fiber-based NICE-OHMS,” J. Opt. Soc. Am. B 28, 2797–2805 (2011).

Siller, B. M.

Slemr, F.

P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

van Helden, J. H.

van Leeuwen, N. J.

Wang, J.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

Werle, P.

P. Werle, “Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence,” Appl. Phys. B 102, 313–329 (2011).

P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

Wong, N. C.

Ye, J.

C. J. Hood, H. J. Kimble, and J. Ye, “Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity,” Phys. Rev. A 64, 033804 (2001).

L. S. Ma, J. Ye, P. Dube, and J. L. 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).

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

L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy - Applications to molecular overtones as visible frequency references,” in Laser Spectroscopy XII International Conference (World Scientific, 1995), pp. 199–203.

Zhao, G.

Appl. Phys. B (5)

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).

P. Werle, “Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence,” Appl. Phys. B 102, 313–329 (2011).

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).

A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, “Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection,” Appl. Phys. B 119, 87–96 (2015).

P. Werle, R. Mucke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption-spectroscopy (TDLAS),” Appl. Phys. B 57, 131–139 (1993).

J. Chem. Phys. (1)

J. Bood, A. McIlroy, and D. L. 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(8), 084311 (2006).
[PubMed]

J. Opt. Soc. Am. B (10)

N. C. Wong and J. L. Hall, “Servo control of amplitude-modulation in frequency-modulation spectroscopy - demonstration of shot-noise-limited detection,” J. Opt. Soc. Am. B 2, 1527–1533 (1985).

A. Foltynowicz, I. Silander, and O. Axner, “Reduction of background signals in fiber-based NICE-OHMS,” J. Opt. Soc. Am. B 28, 2797–2805 (2011).

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 10−12 cm−1 Hz-1/2 region,” J. Opt. Soc. Am. B 29, 1305–1315 (2012).

P. Ehlers, A. C. Johansson, I. Silander, A. Foltynowicz, and O. Axner, “Use of etalon-immune distances to reduce the influence of background signals in frequency-modulation spectroscopy and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy,” J. Opt. Soc. Am. B 31, 2938–2945 (2014).

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

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This implies that l2 and t2 could be assessed to 13 and 44 ppm, respectively.

It should be noted for the case of two different mirrors no such general parameter was found; it is however obvious that a combination of two different mirrors opens up for tailoring the system properties (i.e. the signal and power ratios) more freely.

For the case when Rc is (close to) zero the reflected NICE-OHMS signal cannot be considered to be given by a product of a spectral component of the laser beam that is affected by the molecules in the cavity and a component that is unaffected of this, as is assumed when the ordinary expressions for FMS or NICE-OHMS are derived, but rather by a product of two small molecule-induced entities. However, since Rc > 0 for the case with an impendence unbalanced cavity (as is considered in this work), we still consider Eq. (9) to be valid.

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Figures (6)

Fig. 1
Fig. 1 Schematic illustration of the nomenclature used for the differential NICE-OHMS realization presented in this work. The various entities are defined in the text. DM: Demodulation; Diff: Subtraction of the reflection signal (weighted by the factor a) from the transmitted signal.
Fig. 2
Fig. 2 Simulations of some of the properties of a FP cavity constructed by two identical mirrors. Panel (a): left y-axis: normalized transmitted and reflected power, P tran / P in MM and P refl / P in MM , respectively; right y-axis: normalized NICE-OHMS background signals in transmission and reflection, i.e. S BG tran / S BG tran | F l 2 /π=0 and S BG refl / S BG tran | F l 2 /π=0 , respectively; Panel (b): normalized molecular NICE-OHMS signals in transmission and reflection, i.e. S mol tran / S mol tran | F l 2 /π=0 and S mol refl / S mol tran | F l 2 /π=0 . In both panels, the black solid and the red dashed curves represent transmission and reflection, respectively. The three vertical dotted lines represent F l 2 /π values of 0.02, 0.23, and 0.5.
Fig. 3
Fig. 3 Simulations of the factor a by which the reflection NICE-OHMS signal needs to be multiplied before being subtracted from the transmission signal to yield a differential NICE-OHMS signal that is not affected by any drifts. The four solid curves represent different relative amounts of NMM light, expressed in term of ε values, viz. 0, 0.1, 0.2, and 0.3 (as indicated). The vertical lines have the same meaning as in Fig. 2.
Fig. 4
Fig. 4 Schematic illustration of the NICE-OHMS instrumentation. EDFL, Er-doped fiber laser; f-AOM, fiber-coupled acousto-optic modulator; f-POL, fiber-coupled polarizer; f-EOM, fiber-coupled electro-optic modulator; f-C, fiber-coupled collimator; λ/2, half-wave plate; PBS, polarizing beam splitter; λ/4, quarter-wave plate; PD1-2, photodiodes; PS, power splitter; PDH servo, servo for the Pound-Drever-Hall locking; DVB servo, servo for the DeVoe-Brewer locking.
Fig. 5
Fig. 5 The panels (a), (b), and (c) show, by the black solid curves, the transmission, reflection, and differential NICE-OHMS signals (the latter using a value for a of − 4.2) from 10 ppm of C2H2 in N2 at 100 mTorr detected at 1531.5877 nm, which corresponds to an absorption coefficient on resonance, α 0 , of 1.6 × 10−8 cm−1. The panels (d), (e), and (f) illustrate the drift of the background over 2 hours, represented by the difference between two empty cavity NICE-OHMS signals measured at two instances, separated by 2 hours, for the transmission, reflection and differential signals respectively. The signal drifts in panel (d) - (f) are given relative to the peak to peak of the corresponding signals in the panels (a) - (c). In all cases, the dotted red curves show the corresponding fits. The assessed values of α 0 retrieved by the fits in the panels (d) - (f), which are measures of the drift of the background signal, are given in lower parts of the panels. Note that this drift is one order of magnitude smaller for the differential NICE-OHMS than for the other two signals.
Fig. 6
Fig. 6 The Allan-Werle plot of the transmission, the reflection, and two differential NICE-OHMS signals (blue, red, and green and black curves, respectively), where the latter two were constructed as S tot tran a S tot refl , with a taken as −4.2 and −5.5, respectively.

Equations (22)

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χ q,j c,tran,mol =r t 2 e δ j mol ϕ j mol i e φ j 0 i 1 r 2 e 2 δ j mol 2 ϕ j mol i e 2 φ j 0 i =r (1 r 2 l 2 ) e δ j mol ϕ j mol i e φ j 0 i 1 r 2 e 2 δ j mol 2 ϕ j mol i e 2 φ j 0 i
χ q,j c,refl,mol =r 1(1 l 2 ) e 2 δ j mol 2 ϕ j mol i e 2 φ j 0 i 1 r 2 e 2 δ j mol 2 ϕ j mol i e 2 φ j 0 i ,
φ j 0 =( q+ ν mod ν FSR j )π+ π ς j 0 ν FSR 0 ,
T c = r 2 ( t 2 l 2 + t 2 ) 2 = ( 1 F l 2 π ) 2
R c = r 2 ( l 2 l 2 + t 2 ) 2 = ( F l 2 π ) 2 ,
P tran = P tran MM = T c P in MM
P refl = P refl MM + P refl NMM =( R c +ε ) P in MM ,
S mol tran = (1) ν mod ν FSR η V tran 2F π J 0 J 1 χ ¯ mol NO α 0 L T c 1+ε P in
S mol refl = η V refl 2F π J 0 J 1 χ ¯ mol NO α 0 L R c T c 1+ε P in .
χ ¯ mol NO =( χ ¯ 1 mol,abs χ ¯ 1 mol,abs )sin θ m +( χ ¯ 1 mol,disp 2 χ ¯ 0 mol,disp + χ ¯ 1 mol,disp )cos θ m ,
P in = P in MM + P in NMM =(1+ε) P in MM .
S mol refl = (1) ν mod ν FSR η V refl η V tran R c T c S mol tran .
S BG tran = (1) ν mod ν FSR η V tran J 0 J 1 χ ¯ BG NO T c 1+ε P in
S BG refl = η V refl J 0 J 1 χ ¯ BG NO R c +ε 1+ε P in ,
S BG refl = (1) ν mod ν FSR η V refl η V tran P refl P tran S BG tran = (1) ν mod ν FSR η V refl η V tran R c +ε T c S BG tran = 1 a S BG tran ,
S tot tran = S BG tran + S mol tran
S tot refl = S BG refl + S mol refl .
S diff = S tot tran a S tot refl = R c +ε R c +ε S mol tran = (F l 2 /π)+ε (F l 2 /π) 2 +ε S mol tran ,
F l 2 π = P in P refl P tran P in P refl + P tran .
ε= P in P tran T c 1= P in P tran ( 1 F l 2 π ) 2 1= 4 P in P tran ( P in P refl + P tran ) 2 1.
( α 0 ) SN tran = π FL 1 J 0 J 1 χ ¯ mol NO eΔf η I tran P tran ,
( α 0 ) SN refl ( α 0 ) SN tran = 1+ε ( π F l 2 ) 2 .

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