Abstract

Using the z-scan technique, we have measured the self-induced absorptive and refractive nonlinear behavior of hot atomic rubidium vapor within the Doppler profile of the D2 line. We observe large nonlinear amplitude and phase effects with only tens of microwatts of incident power. Our results are in good agreement with numerical calculations based on an analytic model of a Doppler-broadened two-level system.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
    [CrossRef]
  2. D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
    [CrossRef]
  3. J. E. Bjorkholm and A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
    [CrossRef]
  4. G. A. Swartzlander, H. Yin, and A. E. Kaplan, “Self-bending of a cw laser beam in sodium vapor,” Opt. Lett. 13, 1011–1013 (1988).
    [CrossRef] [PubMed]
  5. J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
    [CrossRef]
  6. D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
    [CrossRef]
  7. Y. Shevy and M. Rosenblum, “Parametric four-wave mixing processes in sodium vapor,” Opt. Lett. 12, 257–259 (1987).
    [CrossRef] [PubMed]
  8. R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
    [CrossRef]
  9. S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
    [CrossRef]
  10. Hai Wang, D. Goorskey, and Min Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27, 258–260 (2002).
    [CrossRef]
  11. A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
    [CrossRef]
  12. R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
    [CrossRef]
  13. J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
    [CrossRef]
  14. D. H. Close, “Strong-field saturation effects in laser media,” Phys. Rev. 153, 360–371 (1967).
    [CrossRef]
  15. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
  16. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, England, 1990).
  17. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  18. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
    [CrossRef]
  19. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (U.S. GPO, Washington, D.C., 1968), p. 298.
  20. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1, 13–15 (1977).
    [CrossRef] [PubMed]
  21. G. P. Agrawal and M. Lax, “End correction in the quasi-fast Hankel transform for optical-propagation problems,” Opt. Lett. 6, 171–173 (1981).
    [CrossRef] [PubMed]

2002 (2)

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Hai Wang, D. Goorskey, and Min Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27, 258–260 (2002).
[CrossRef]

2001 (1)

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

2000 (1)

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

1999 (1)

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

1981 (2)

G. P. Agrawal and M. Lax, “End correction in the quasi-fast Hankel transform for optical-propagation problems,” Opt. Lett. 6, 171–173 (1981).
[CrossRef] [PubMed]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

1977 (1)

1976 (1)

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
[CrossRef]

1974 (1)

J. E. Bjorkholm and A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

1972 (1)

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

1971 (1)

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

1970 (1)

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

1967 (1)

D. H. Close, “Strong-field saturation effects in laser media,” Phys. Rev. 153, 360–371 (1967).
[CrossRef]

Agarwal, G. S.

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

Agrawal, G. P.

Andersen, J. A.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

Armstrong, J. A.

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

Ashkin, A.

J. E. Bjorkholm and A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

Bhowmick, G. K.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm and A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

Bjorklund, G. C.

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

Boyd, R. W.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

Close, D. H.

D. H. Close, “Strong-field saturation effects in laser media,” Phys. Rev. 153, 360–371 (1967).
[CrossRef]

Dasgupta, K.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Drummond, P. D.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

Eckardt, R. C.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
[CrossRef]

Ficek, Z.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

Friese, M. E. J.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

Goorskey, D.

Grischkowsky, D.

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

Harris, S. E.

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

Harter, D. J.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

Heckenberg, N. R.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

Kaplan, A. E.

Kapoor, R.

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

Kundu, S.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Kung, A. H.

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

Lax, M.

Lehmberg, R. H.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
[CrossRef]

Miles, R. B.

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

Nair, S. K. S.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Narum, P.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

Pal, T. B.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Ray, A. K.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Raymer, M. G.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

Reintjes, J.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
[CrossRef]

Rosenblum, M.

Rubinsztein-Dunlop, H.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Sasikumar, S.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Shevy, Y.

Siegman, A. E.

Sinha, S.

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Swartzlander, G. A.

Truscott, A. G.

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Wang, Hai

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

Xiao, Min

Yin, H.

Young, J. F.

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

Opt. Commun. (1)

S. Sinha, G. K. Bhowmick, S. Kundu, S. Sasikumar, S. K. S. Nair, T. B. Pal, A. K. Ray, and K. Dasgupta, “A Z-scan study of nonlinear refraction in sodium vapor,” Opt. Commun. 203, 427–434 (2002).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. (1)

D. H. Close, “Strong-field saturation effects in laser media,” Phys. Rev. 153, 360–371 (1967).
[CrossRef]

Phys. Rev. A (4)

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

J. A. Andersen, M. E. J. Friese, A. G. Truscott, Z. Ficek, P. D. Drummond, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Light guiding light: Nonlinear refraction in rubidium vapor,” Phys. Rev. A 63, 023820 (2001).
[CrossRef]

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Negative nonlinear susceptibility of cesium vapor around 1.06 μm,” Phys. Rev. A 13, 1095–1103 (1976).
[CrossRef]

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6, 1566–1570 (1972).
[CrossRef]

Phys. Rev. Lett. (5)

J. E. Bjorkholm and A. Ashkin, “cw self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[CrossRef]

J. F. Young, G. C. Bjorklund, A. H. Kung, R. B. Miles, and S. E. Harris, “Third-harmonic generation in phase-matched Rb vapor,” Phys. Rev. Lett. 27, 1551–1553 (1971).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, “Four-wave parametric amplification of Rabi sidebands in sodium,” Phys. Rev. Lett. 46, 1192–1195 (1981).
[CrossRef]

D. Grischkowsky, “Self-focusing of light by potassium vapor,” Phys. Rev. Lett. 24, 866–869 (1970).
[CrossRef]

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438–1441 (1999).
[CrossRef]

Other (3)

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

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, England, 1990).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (U.S. GPO, Washington, D.C., 1968), p. 298.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Experimental configuration for the z-scan measurement: L1 and L2, lasers 1 and 2; SAS, saturated absorption spectroscopy lock; C, chopper wheel; C1 and C2, fiber-coupling lenses; SMF, single-mode fiber; A, aperture; PD, photodiode; LA, lock-in amplifier; FPD, fast photodiode.

Fig. 2
Fig. 2

Open-aperture scan at 300 MHz to the blue of the 85RbF=3F line, with fit from the Doppler-broadened two-level model. The scan at 300 MHz to the red is very similar.

Fig. 3
Fig. 3

Closed-aperture scan at 300 MHz to the blue of the 85RbF=3F line. The theory curve is calculated directly from the fit parameters found in the corresponding open scan, with no adjustable parameters. The typical systematic error mostly results from residual beam astigmatism and uncertainties about the aperture size.

Fig. 4
Fig. 4

As above in Fig. 3, for a detuning of 300 MHz to the red.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

α(x, I)=α0exp(-x2)(1+I/Is)1/2-aπ [1-2xF(x)],
n(x, I)=1-α0cωa2 x exp(-x2)(1+I/Is)1/2-F(x)π.
F(x)=exp(-x2)0xexp(+t2)dt.

Metrics