Abstract

We experimentally investigate ultralow-power saturation of the rubidium D2 transitions using a tapered optical fiber (TOF) suspended in a warm Rb vapor. A direct comparison of power-dependent absorption measurements for the TOF system with those obtained in a standard free-space vapor cell system highlights the differences in saturation behavior for the two systems. The effects of hyperfine pumping in the TOF system are found to be minimized due to the short atomic transit times through the highly confined evanescent optical mode guided by the TOF. The TOF system data are well-fit by a relatively simple empirical absorption model that indicates nanoWatt-level saturation powers.

© 2014 Optical Society of America

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  1. S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
    [CrossRef]
  2. T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
    [CrossRef]
  3. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of sub-wavelength diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004).
    [CrossRef]
  4. S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
    [CrossRef]
  5. K. Salit, M. Salit, S. Krishnamurthy, Y. Wang, P. Kumar, and M. S. Shahriar, “Ultra-low power, Zeno effect based optical modulation in a degenerate V-system with a tapered nano fiber in atomic vapor,” Opt. Express 19, 22874 (2011).
    [CrossRef]
  6. M. M. Lai, J. D. Franson, and T. B. Pittman, “Transmission degradation and preservation for tapered optical fibers in rubidium vapor,” Appl. Opt. 52, 2595–2601 (2013).
    [CrossRef]
  7. V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
    [CrossRef]
  8. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, 2003).
  9. P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
    [CrossRef]
  10. T. M. Stace and A. N. Luiten, “Theory of spectroscopy in an optically pumped effusive vapor,” Phys. Rev. A 81, 033848 (2010).
    [CrossRef]
  11. D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
    [CrossRef]
  12. B. E. Sherlock and I. G. Hughes, “How weak is a weak probe laser in spectroscopy?” Am. J. Phys. 77, 111–115 (2009).
    [CrossRef]
  13. G. Moon and H.-R. Noh, “A comparison of the dependence of saturated absorption signals on pump beam diameter and intensity,” J. Opt. Soc. Am. B 25, 2101–2106 (2008).
    [CrossRef]
  14. G. Moon and H.-R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294–298 (2008).
    [CrossRef]
  15. T. Lindvall and I. Tittonen, “Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy,” Phys. Rev. A 80, 032505 (2009).
    [CrossRef]
  16. C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
    [CrossRef]
  17. M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
    [CrossRef]
  18. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
    [CrossRef]
  19. A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
    [CrossRef]
  20. H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
    [CrossRef]
  21. M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
    [CrossRef]
  22. T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
    [CrossRef]
  23. A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
    [CrossRef]
  24. A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
    [CrossRef]
  25. J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
    [CrossRef]
  26. I. E. Olivares, “Transmission of tunable diode laser emission, through rubidium vapor, as a function of laser intensity,” J. Opt. Soc. Am. B 30, 945–949 (2013).
    [CrossRef]
  27. A. Yariv, Quantum Electronics (Wiley, 1989).
  28. A. Corney, Atomic and Laser Spectroscopy (Oxford University, 2006).
  29. D. A. Steck, “Rubidium 85 D line data,” 2012, http://steck.us/alkalidata/ .
  30. C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
    [CrossRef]

2013 (6)

T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
[CrossRef]

M. M. Lai, J. D. Franson, and T. B. Pittman, “Transmission degradation and preservation for tapered optical fibers in rubidium vapor,” Appl. Opt. 52, 2595–2601 (2013).
[CrossRef]

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

I. E. Olivares, “Transmission of tunable diode laser emission, through rubidium vapor, as a function of laser intensity,” J. Opt. Soc. Am. B 30, 945–949 (2013).
[CrossRef]

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

2012 (3)

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
[CrossRef]

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
[CrossRef]

2011 (1)

2010 (3)

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

T. M. Stace and A. N. Luiten, “Theory of spectroscopy in an optically pumped effusive vapor,” Phys. Rev. A 81, 033848 (2010).
[CrossRef]

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

2009 (2)

T. Lindvall and I. Tittonen, “Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy,” Phys. Rev. A 80, 032505 (2009).
[CrossRef]

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe laser in spectroscopy?” Am. J. Phys. 77, 111–115 (2009).
[CrossRef]

2008 (5)

G. Moon and H.-R. Noh, “A comparison of the dependence of saturated absorption signals on pump beam diameter and intensity,” J. Opt. Soc. Am. B 25, 2101–2106 (2008).
[CrossRef]

G. Moon and H.-R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294–298 (2008).
[CrossRef]

H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
[CrossRef]

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

2006 (1)

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

2004 (2)

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of sub-wavelength diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004).
[CrossRef]

1997 (1)

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

1996 (1)

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
[CrossRef]

1992 (1)

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

Abbott, P. C.

Abdolvand, A.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Adams, C. S.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

Anstie, J.

Anstie, J. D.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

Barbe, R.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Barbieri, M.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Beausoleil, R. G.

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Benabid, F.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

Bhagwat, A. R.

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Birks, T.

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

Champion, T. F. M.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Chormaic, S. N.

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Corney, A.

A. Corney, Atomic and Laser Spectroscopy (Oxford University, 2006).

Deasy, K.

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Demtröder, W.

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, 2003).

Ducloy, M.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

England, D. G.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Fichet, M.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Franson, J. D.

M. M. Lai, J. D. Franson, and T. B. Pittman, “Transmission degradation and preservation for tapered optical fibers in rubidium vapor,” Appl. Opt. 52, 2595–2601 (2013).
[CrossRef]

T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
[CrossRef]

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
[CrossRef]

Gaeta, A. L.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
[CrossRef]

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Ge, C.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

Ghosh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Goh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Gorris-Neveux, M.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Hall, M.

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Hendrickson, S. M.

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
[CrossRef]

Huennekens, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
[CrossRef]

Hughes, I. G.

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe laser in spectroscopy?” Am. J. Phys. 77, 111–115 (2009).
[CrossRef]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

Jin, X. M.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Jones, D. E.

T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
[CrossRef]

Keller, J. C.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Kirby, B. J.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Kolthammer, W. S.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Krishnamurthy, S.

Kumar, P.

K. Salit, M. Salit, S. Krishnamurthy, Y. Wang, P. Kumar, and M. S. Shahriar, “Ultra-low power, Zeno effect based optical modulation in a degenerate V-system with a tapered nano fiber in atomic vapor,” Opt. Express 19, 22874 (2011).
[CrossRef]

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Lai, M. M.

M. M. Lai, J. D. Franson, and T. B. Pittman, “Transmission degradation and preservation for tapered optical fibers in rubidium vapor,” Appl. Opt. 52, 2595–2601 (2013).
[CrossRef]

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

Li, Y.

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

Light, P. S.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

Lindvall, T.

T. Lindvall and I. Tittonen, “Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy,” Phys. Rev. A 80, 032505 (2009).
[CrossRef]

Londero, P.

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

Lou, J.

Luiten, A. N.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

T. M. Stace and A. N. Luiten, “Theory of spectroscopy in an optically pumped effusive vapor,” Phys. Rev. A 81, 033848 (2010).
[CrossRef]

Lurie, A.

Mazur, E.

Michelberger, P. S.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Monnot, P.

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Moon, G.

G. Moon and H.-R. Noh, “A comparison of the dependence of saturated absorption signals on pump beam diameter and intensity,” J. Opt. Soc. Am. B 25, 2101–2106 (2008).
[CrossRef]

G. Moon and H.-R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294–298 (2008).
[CrossRef]

Namiotka, R. K.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
[CrossRef]

Noh, H.-R.

G. Moon and H.-R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294–298 (2008).
[CrossRef]

G. Moon and H.-R. Noh, “A comparison of the dependence of saturated absorption signals on pump beam diameter and intensity,” J. Opt. Soc. Am. B 25, 2101–2106 (2008).
[CrossRef]

Nunn, J.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Olivares, I. E.

Pati, G. S.

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Perrella, C.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

Pittman, T. B.

T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
[CrossRef]

M. M. Lai, J. D. Franson, and T. B. Pittman, “Transmission degradation and preservation for tapered optical fibers in rubidium vapor,” Appl. Opt. 52, 2595–2601 (2013).
[CrossRef]

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

Renshaw, C. K.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

Rigal, B.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Russell, P. S. J.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Sagle, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
[CrossRef]

Saha, K.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
[CrossRef]

Salit, K.

K. Salit, M. Salit, S. Krishnamurthy, Y. Wang, P. Kumar, and M. S. Shahriar, “Ultra-low power, Zeno effect based optical modulation in a degenerate V-system with a tapered nano fiber in atomic vapor,” Opt. Express 19, 22874 (2011).
[CrossRef]

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Salit, M.

Shahriar, M. S.

K. Salit, M. Salit, S. Krishnamurthy, Y. Wang, P. Kumar, and M. S. Shahriar, “Ultra-low power, Zeno effect based optical modulation in a degenerate V-system with a tapered nano fiber in atomic vapor,” Opt. Express 19, 22874 (2011).
[CrossRef]

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Sherlock, B. E.

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe laser in spectroscopy?” Am. J. Phys. 77, 111–115 (2009).
[CrossRef]

Siddons, P.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

Slepkov, A.

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

Smith, D. A.

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

Spillane, S. M.

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

Sprague, M. R.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Stace, T. M.

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

A. Lurie, P. S. Light, J. Anstie, T. M. Stace, P. C. Abbott, F. Benabid, and A. N. Luiten, “Saturation spectroscopy of iodine in hollow-core optical fiber,” Opt. Express 20, 11906 (2012).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

T. M. Stace and A. N. Luiten, “Theory of spectroscopy in an optically pumped effusive vapor,” Phys. Rev. A 81, 033848 (2010).
[CrossRef]

Tittonen, I.

T. Lindvall and I. Tittonen, “Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy,” Phys. Rev. A 80, 032505 (2009).
[CrossRef]

Tiwari, V. B.

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Tong, L.

Venkataraman, V.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
[CrossRef]

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

Walmsley, I. A.

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Wang, Y.

Ward, J. M.

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Watkins, A.

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

You, H.

H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
[CrossRef]

Am. J. Phys. (2)

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631–637 (2004).
[CrossRef]

B. E. Sherlock and I. G. Hughes, “How weak is a weak probe laser in spectroscopy?” Am. J. Phys. 77, 111–115 (2009).
[CrossRef]

Appl. Opt. (1)

J. Lightwave Technol. (1)

T. Birks and Y. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (2)

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B 41, 155004 (2008).
[CrossRef]

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629–2643 (1996).
[CrossRef]

Nat. Photonics (1)

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2012).
[CrossRef]

New J. Phys. (1)

M. R. Sprague, D. G. England, A. Abdolvand, J. Nunn, X. M. Jin, W. S. Kolthammer, M. Barbieri, B. Rigal, P. S. Michelberger, T. F. M. Champion, P. S. J. Russell, and I. A. Walmsley, “Efficient optical pumping and high optical depth in a hollow-core photonic-crystal fibre for a broadband quantum memory,” New J. Phys. 15, 055013 (2013).
[CrossRef]

Opt. Commun. (2)

G. Moon and H.-R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294–298 (2008).
[CrossRef]

M. Gorris-Neveux, P. Monnot, M. Fichet, M. Ducloy, R. Barbe, and J. C. Keller, “Doppler-free reflection spectroscopy of rubidium D1 line in optically dense vapour,” Opt. Commun. 134, 85–90 (1997).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (7)

T. B. Pittman, D. E. Jones, and J. D. Franson, “Ultralow-power nonlinear optics using tapered optical fibers in metastable xenon,” Phys. Rev. A 88, 053804 (2013).
[CrossRef]

T. M. Stace and A. N. Luiten, “Theory of spectroscopy in an optically pumped effusive vapor,” Phys. Rev. A 81, 033848 (2010).
[CrossRef]

T. Lindvall and I. Tittonen, “Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy,” Phys. Rev. A 80, 032505 (2009).
[CrossRef]

C. Perrella, P. S. Light, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution optical spectroscopy in a hollow-core photonic crystal fiber,” Phys. Rev. A 85, 012518 (2012).
[CrossRef]

A. Slepkov, A. R. Bhagwat, V. Venkataraman, P. Londero, and A. L. Gaeta, “Spectroscopy of Rb atoms in hollow-core fibers,” Phys. Rev. A 81, 053825 (2010).
[CrossRef]

H. You, S. M. Hendrickson, and J. D. Franson, “Analysis of enhanced two-photon absorption in tapered optical fibers,” Phys. Rev. A 78, 053803 (2008).
[CrossRef]

C. Perrella, P. S. Light, J. D. Anstie, T. M. Stace, F. Benabid, and A. N. Luiten, “High-resolution two-photon spectroscopy of rubidium within a confined geometry,” Phys. Rev. A 87, 103818 (2013).
[CrossRef]

Phys. Rev. Lett. (3)

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, “Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).
[CrossRef]

S. M. Spillane, G. S. Pati, K. Salit, M. Hall, P. Kumar, R. G. Beausoleil, and M. S. Shahriar, “Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor,” Phys. Rev. Lett. 100, 233602 (2008).
[CrossRef]

S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. 105, 173602 (2010).
[CrossRef]

Proc. SPIE (1)

A. Watkins, V. B. Tiwari, J. M. Ward, K. Deasy, and S. N. Chormaic, “Observation of Zeeman shift in the rubidium D2 line using an optical nanofiber in vapor,” Proc. SPIE 8785, 87850S (2013).
[CrossRef]

Other (4)

A. Yariv, Quantum Electronics (Wiley, 1989).

A. Corney, Atomic and Laser Spectroscopy (Oxford University, 2006).

D. A. Steck, “Rubidium 85 D line data,” 2012, http://steck.us/alkalidata/ .

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

Overview of the TOF system. The data points are SEM measurements of the diameter used to profile the TOF (represented by the blue shaded area). The red shaded area represents a calculation of the HE11 optical mode guided by the TOF (the mode is shown as the diameter in which half of the total power is confined) [3]. Note that the aspect ratio of the figure is compressed by a factor of 104; the key point is the propagation of a very tightly confined evanescent field over a very long interaction length in a surrounding Rb vapor.

Fig. 2.
Fig. 2.

Block diagram of the experimental setup highlighting the vapor cell system and the TOF system. The entire apparatus is fiber-based (red lines), except for the free-space beam passing through the Rb vapor cell. Detectors D1 (input) and D2 (output) are used to record transmission spectra for the vapor cell system, while detectors D3 and D4 are used for the TOF system. Variable attenuators (VAs) are used to control the input powers to the two systems. Additional details on the TOF vacuum system can be found in [6].

Fig. 3.
Fig. 3.

(a) Simplified energy level diagram for the relevant D2 transitions in Rb85 and Rb87; the excited-state hyperfine splittings (F) are closely spaced and not resolved due to Doppler broadening. For convenience, the transitions (and corresponding absorption dips) are labeled 1–4. Plot (b) shows transmission spectra obtained in the vapor cell system, while plot (c) shows corresponding data simultaneously obtained in the TOF system. A comparison of (b) and (c) highlights the differences in transit time broadening and hyperfine pumping rates for these two systems.

Fig. 4.
Fig. 4.

Example of calculated population versus time for the hyperfine ground-state |c while driving the |a|b transition corresponding to dip 3 (see inset). The blue, purple, red, and green curves (left to right) correspond to driving intensities of 10, 1, 0.1, and 0.01 Isat, respectively. Here, Isat is given by the nominal Rb value of 1.6mW/cm2. In all cases, the key point is that the hyperfine pumping time is of the order of μs. This is comparable to the atomic transit times in vapor cell experiments but much longer than the ns transit times in TOF experiments.

Fig. 5.
Fig. 5.

Comparison of the measured transmission of dips 1–4 at powers below saturation for (a) the vapor cell system with a large (2mm) diameter beam, and (b) the TOF system. The effects of hyperfine pumping are clearly seen in the vapor cell data of (a), where dip 3 (dip 4) appears to “saturate” more quickly than dip 2 (dip 1). In contrast, the effects of hyperfine pumping are not evident in the TOF system data of (b). The error bars on the data are comparable to the data point size. The solid lines are simply guides to the eye.

Fig. 6.
Fig. 6.

Comparison of the measured transmission of dip 2 for (a) the vapor cell system, and (b) the TOF system. The wide range of input powers (μW for the vapor cell, nW for the TOF) facilitate fitting the data to a simple nonlinear transmission model (described in the main text). The green curves correspond to r=1 and the blue curves to r=1/2. Note the failure of both curves in the vapor cell system in (a) and the good agreement of the green curve with the TOF data in (b). This empirical nonlinear absorption model provides a saturation power of (61±3) nW for the TOF system. The dashed red lines correspond to ordinary linear absorption models.

Equations (1)

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αNLαo(1+P/Psat)r,

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