Abstract

We report the calculations of vectorial nonlinear properties of rubidium vapor for Rb87 D2 transition at moderate intensities. The results are compared with self-rotation and diffraction experiments. Different from Kerr nonlinearity, optimal intensity exists here, which depends on beam geometry. For intensities close to the optimal, the vectorial mechanism is much more efficient than a scalar one, and strong self-action for wide beams can be obtained with it.

© 2012 Optical Society of America

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References

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  1. P. Zerom and R. W. Boyd, “Self-focusing, conical emission, and other self-action effects in atomic vapors,” in Self-focusing: Past and Present, Vol. 114 of Topics in Applied Physics, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., (Springer Science+Business Media, 2009), pp. 231–251.
  2. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).
  3. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  4. E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 1996), Vol. 35, pp. 257–354.
  5. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
    [CrossRef]
  6. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
    [CrossRef]
  7. E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
    [CrossRef]
  8. I. H. Agha, G. Messin, and P. Grangier, “Generation of pulsed and continuos-wave squeezed light with (87)Rb vapor,” Opt. Express 18, 4198–4205 (2010).
    [CrossRef]
  9. C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36, 2979–2981 (2011).
    [CrossRef]
  10. N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
    [CrossRef]
  11. R. Zhang, J. A. Greenberg, M. C. Fischer, and D. J. Gauthier, “Controllable ultrabroadband slow light in a warm rubidium vapor,” J. Opt. Soc. Am. B 28, 2578–2583 (2011).
    [CrossRef]
  12. S. R. Shin, and H.-R. Noh, “Doppler spectroscopy of arbitrarily polarized light in rubidium,” Opt. Commun. 284, 1243–1246 (2011).
    [CrossRef]
  13. S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
    [CrossRef]
  14. G. Moon and H. Noh, “Analytic solutions for the saturated absorption spectra,” J. Opt. Soc. Am. B 25, 701–711 (2008).
    [CrossRef]
  15. N. Korneev and O. Benavides, “Mechanisms of holographic recording in rubidium vapor close to resonance,” J. Opt. Soc. Am. B 25, 1899–1906 (2008).
    [CrossRef]
  16. N. Korneev and O. Benavides, “Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour,” J. Mod. Opt. 56, 1194–1198 (2009).
    [CrossRef]
  17. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge, 2004).
  18. G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches (Springer Verlag, 1974).
  19. K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
    [CrossRef]
  20. J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
    [CrossRef]
  21. E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33, 1213–1215 (2008).
    [CrossRef]
  22. N. Korneev, “Nonlinearity enhancement in rubidium vapour with vectorial mechanism,” Proc. SPIE 8011, 801137 (2011).
    [CrossRef]

2011 (5)

S. R. Shin, and H.-R. Noh, “Doppler spectroscopy of arbitrarily polarized light in rubidium,” Opt. Commun. 284, 1243–1246 (2011).
[CrossRef]

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

N. Korneev, “Nonlinearity enhancement in rubidium vapour with vectorial mechanism,” Proc. SPIE 8011, 801137 (2011).
[CrossRef]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, and W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36, 2979–2981 (2011).
[CrossRef]

R. Zhang, J. A. Greenberg, M. C. Fischer, and D. J. Gauthier, “Controllable ultrabroadband slow light in a warm rubidium vapor,” J. Opt. Soc. Am. B 28, 2578–2583 (2011).
[CrossRef]

2010 (1)

2009 (2)

N. Korneev and O. Benavides, “Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour,” J. Mod. Opt. 56, 1194–1198 (2009).
[CrossRef]

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

2008 (3)

2007 (1)

N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
[CrossRef]

2005 (2)

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2003 (1)

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
[CrossRef]

2002 (1)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

1993 (1)

Agarwal, G. S.

G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches (Springer Verlag, 1974).

Agha, I. H.

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 1996), Vol. 35, pp. 257–354.

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge, 2004).

Benavides, O.

N. Korneev and O. Benavides, “Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour,” J. Mod. Opt. 56, 1194–1198 (2009).
[CrossRef]

N. Korneev and O. Benavides, “Mechanisms of holographic recording in rubidium vapor close to resonance,” J. Opt. Soc. Am. B 25, 1899–1906 (2008).
[CrossRef]

Boyd, R. W.

P. Zerom and R. W. Boyd, “Self-focusing, conical emission, and other self-action effects in atomic vapors,” in Self-focusing: Past and Present, Vol. 114 of Topics in Applied Physics, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., (Springer Science+Business Media, 2009), pp. 231–251.

Brezger, B.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
[CrossRef]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Castin, Y.

Chaudhuri, C.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Clark, S. M.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

Dalibard, J.

Dawes, A. M. C.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

Fischer, M. C.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Gauthier, D. J.

R. Zhang, J. A. Greenberg, M. C. Fischer, and D. J. Gauthier, “Controllable ultrabroadband slow light in a warm rubidium vapor,” J. Opt. Soc. Am. B 28, 2578–2583 (2011).
[CrossRef]

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

Gawlik, W.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Ghosh, P. N.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Grangier, P.

Greenberg, J. A.

Hossain, M. M.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Hudelist, F.

Illing, L.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Jing, J.

Kimball, D. F.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Korneev, N.

N. Korneev, “Nonlinearity enhancement in rubidium vapour with vectorial mechanism,” Proc. SPIE 8011, 801137 (2011).
[CrossRef]

N. Korneev and O. Benavides, “Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour,” J. Mod. Opt. 56, 1194–1198 (2009).
[CrossRef]

N. Korneev and O. Benavides, “Mechanisms of holographic recording in rubidium vapor close to resonance,” J. Opt. Soc. Am. B 25, 1899–1906 (2008).
[CrossRef]

Lezama, A.

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

Liu, C.

Lvovsky, A. I.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Messin, G.

Mikhailov, E. E.

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33, 1213–1215 (2008).
[CrossRef]

Mitra, S.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Mølmer, K.

Moon, G.

Noel, T. W.

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

Noh, H.

Noh, H.-R.

S. R. Shin, and H.-R. Noh, “Doppler spectroscopy of arbitrarily polarized light in rubidium,” Opt. Commun. 284, 1243–1246 (2011).
[CrossRef]

Novikova, I.

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33, 1213–1215 (2008).
[CrossRef]

Pattabiraman, M.

N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
[CrossRef]

Poddar, P.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Pooser, R. C.

Ram, N.

N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
[CrossRef]

Ray, B.

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

Ries, J.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
[CrossRef]

Rochester, S. M.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

Shin, S. R.

S. R. Shin, and H.-R. Noh, “Doppler spectroscopy of arbitrarily polarized light in rubidium,” Opt. Commun. 284, 1243–1246 (2011).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

Vijayan, C.

N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
[CrossRef]

Weis, A.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Yashchuk, V. V.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

Zerom, P.

P. Zerom and R. W. Boyd, “Self-focusing, conical emission, and other self-action effects in atomic vapors,” in Self-focusing: Past and Present, Vol. 114 of Topics in Applied Physics, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., (Springer Science+Business Media, 2009), pp. 231–251.

Zhang, R.

Zhang, W.

Zhou, L.

Zhou, Z.

Chem. Phys. Lett. (1)

S. Mitra, M. M. Hossain, P. Poddar, C. Chaudhuri, B. Ray, and P. N. Ghosh, “Standing wave pump field induced coherent non-linear resonances in rubidium vapor,” Chem. Phys. Lett. 513, 173–178 (2011).
[CrossRef]

J. Mod. Opt. (2)

N. Korneev and O. Benavides, “Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour,” J. Mod. Opt. 56, 1194–1198 (2009).
[CrossRef]

E. E. Mikhailov, A. Lezama, T. W. Noel, and I. Novikova, “Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors,” J. Mod. Opt. 56, 1985–1992 (2009).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. Conf. Ser. (1)

N. Ram, M. Pattabiraman, and C. Vijayan, “Low field Zeeman magnetometry using rubidium absorption spectroscopy,” J. Phys. Conf. Ser. 80, 012035 (2007).
[CrossRef]

Opt. Commun. (1)

S. R. Shin, and H.-R. Noh, “Doppler spectroscopy of arbitrarily polarized light in rubidium,” Opt. Commun. 284, 1243–1246 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental vacuum squeezing in rubidium vapor via self-rotation,” Phys. Rev. A 68, 025801 (2003).
[CrossRef]

Proc. SPIE (1)

N. Korneev, “Nonlinearity enhancement in rubidium vapour with vectorial mechanism,” Proc. SPIE 8011, 801137 (2011).
[CrossRef]

Rev. Mod. Phys. (2)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Science (1)

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium Vapor,” Science 308, 672–674 (2005).
[CrossRef]

Other (5)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 1996), Vol. 35, pp. 257–354.

P. Zerom and R. W. Boyd, “Self-focusing, conical emission, and other self-action effects in atomic vapors,” in Self-focusing: Past and Present, Vol. 114 of Topics in Applied Physics, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., (Springer Science+Business Media, 2009), pp. 231–251.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge, 2004).

G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches (Springer Verlag, 1974).

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Figures (15)

Fig. 1.
Fig. 1.

Cross-phase modulation spectra in Fg=2 line for two intensities (a) 8.54mW/mm2 and (b) 0.53mW/mm2, both with different times of flight. The zero frequency corresponds to Fg=2, Fe=2 transition.

Fig. 2.
Fig. 2.

Cross-phase modulation spectra in Fg=2 line for time of flight 8.2 μs and different intensities.

Fig. 3.
Fig. 3.

Cross-phase modulation spectra for linear polarization, time of flight 8.2 μs, intensity 2.1mW/mm2, and different magnetic fields. The inset shows the maximum absolute value of each spectra in function of magnetic field.

Fig. 4.
Fig. 4.

Curve 1: zero magnetic field, η+. Curve 2: zero magnetic field, η with ellipticity ε=0. Curves 3 and 4: two eigenvalues for ellipticity ε=0.061, and magnetic field B=0.51G. Time of flight 8.2 μs, intensity 2.1mW/mm2.

Fig. 5.
Fig. 5.

Eigenvalues for ellipticity ε=0.061 and different magnetic fields. Time of flight 8.2 μs, intensity 2.1mW/mm2. The inset shows the maximum absolute value of each eigenvalue in function of magnetic field.

Fig. 6.
Fig. 6.

Eigenvalues for ellipticity ε=0.116 and different magnetic fields. Time of flight 8.2 μs, intensity 2.1mW/mm2. The inset shows the maximum absolute value of each eigenvalue in function of magnetic field.

Fig. 7.
Fig. 7.

Fg=1 transition, cross-phase modulation spectra for time of flight 8.2 μs and different intensities.

Fig. 8.
Fig. 8.

Fg=1 transition, curve 1: zero magnetic field, η+. Curve 2: zero magnetic field, η with ellipticity ε=0. Curves 3 and 4: two eigenvalues for ellipticity ε=0.119, and magnetic field B=0.73G. Time of flight 8.2 μs, intensity 0.53mW/mm2.

Fig. 9.
Fig. 9.

Fg=1 transition, eigenvalues for ellipticity ε=0.119, and different magnetic fields. Time of flight 8.2 μs, intensity 0.53mW/mm2. The insert shows the maximum absolute value of each eigenvalue in function of magnetic field.

Fig. 10.
Fig. 10.

Self-rotation signal for different beam powers. The Gaussian beam radius is r=0.82mm. The behavior in Rb87 Fg=2 transition (left spike) qualitatively corresponds to the theoretical curves in Fig. 2.

Fig. 11.
Fig. 11.

Self-rotation signal for different beam powers. Similar to Fig. 10, but the Gaussian beam radius is r=0.17±0.02mm.

Fig. 12.
Fig. 12.

Spectral dependences of pump beam transmission through the cell (fine line) and diffracted wave intensity for different combinations of signal and pump polarizations. We have two signals with polarizations parallel to pump and orthogonal to pump, respectively, both with linear polarization of pump and zero magnetic field. Dashed line is for a pump beam ellipticity 0.07 and a magnetic field B=0.58G. The results in Rb87 Fg=2 transition (left spike) are related to the theoretical curves in Fig. 4.

Fig. 13.
Fig. 13.

Diffraction efficiency in a conjugated beam for B=0, linear pump polarization, and cross-polarized signal beam in function of laser power. Circles: ratio of diffracted beam intensity to input pump beam intensity. Squares: ratio of diffracted beam intensity to output pump intensity. The difference is due to absorption, which is intensity dependent. All values are taken for the laser frequency giving maximal diffracted beam intensity.

Fig. 14.
Fig. 14.

Pump intensity (solid line) and signal intensity (dashed) for P=24mW, T=95°C, pump beam ellipticity 0.07, and magnetic field B=0.56G. Signals are normalized to unity at maximum.

Fig. 15.
Fig. 15.

Far-field images of a beam shape after a cylindrical lens for elliptic pump polarization obtained with 7°. rotation of quarter wave plate. Temperature 98 °C (a) Fg=1 line, zero magnetic field, the signal wave position is marked by an arrow. (b) Modulation instability amplifies the signal and conjugate order, Fg=1 line center, beam power 2.5 mW, magnetic field 1.2 G. (c) Pump beam shape modification for the conditions of image b. (d) For Fg=2 transition the pump is further broken into a number of spots: beam power 27 mW, magnetic field 1.8 G. The vertical size of images corresponds to 20 mrad.

Equations (7)

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

n2I/Δ3.
Pi=Fi(|σ1|,|σ2|)σi=Fi(Ω1,Ω2)σi.
F1Ω1Ω1F1Ω2Ω2F2Ω1Ω1F2Ω2Ω2.
η±=F1Ω1Ω1±F1Ω2Ω2,forΩ1=Ω2=Ω.
tanε=σ2σ1σ2+σ1.
ρt=(i/)[ρ,H]+q=1,0,1CqρCq+12(Cq+Cqρ+ρCq+Cq),
Cq+|Fg,mFg=Γ1/2(1,Fg,q,mFg;Fe,mFe=mFg+q)|Fe,mFe=mFg+q,Cq+|Fe,mFe=0,Cq=(Cq+)*,

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