Abstract

We describe a conical emission process that occurs when two beams of near-resonant light intersect as they pass through sodium vapor. The light is emitted on the surface of a circular cone that is centered on the bisector of the two applied beams and has an angular extent equal to the crossing angle of the two applied beams. We ascribe the origin of this effect to a perfectly phase-matched four-wave mixing process.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. See the feature issue on transverse effects in nonlinear-optical systems, J. Opt. Soc. Am. B 7, 948–1157 (1990),J. Opt. Soc. Am. B 7, 1264–1373 (1990).
  2. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  3. M. T. Gruneisen, K. R. MacDonald, R. W. Boyd, J. Opt. Soc. Am. B 5, 123 (1988); M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, Phys. Rev. A 40, 3464 (1989).
    [CrossRef] [PubMed]
  4. D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
    [CrossRef] [PubMed]
  5. J. Pender, L. Hesselink, IEEE J. Quantum Electron. 25, 395 (1989); J. Opt. Soc. Am. B 7, 1361 (1990).
    [CrossRef]
  6. G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
    [CrossRef]
  7. W. J. Firth, C. Paré, Opt. Lett. 13, 1096 (1988); G. G. Luther, C. J. McKinstrie, J. Opt. Soc. Am. B 7, 1125 (1990).
    [CrossRef] [PubMed]
  8. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
    [CrossRef]
  9. E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
    [CrossRef]
  10. Note that a seeded version of a similar four-wave mixing process was analyzed by A. Khyzniak, V. Kondilenko, Yu. Kucherov, S. Lesnik, S. Odoulov, M. Soskin, J. Opt. Soc. Am. A 1, 169 (1984).
    [CrossRef]
  11. D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970).
    [CrossRef]
  12. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Optical Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 2.

1990 (1)

1989 (1)

J. Pender, L. Hesselink, IEEE J. Quantum Electron. 25, 395 (1989); J. Opt. Soc. Am. B 7, 1361 (1990).
[CrossRef]

1988 (3)

1986 (1)

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

1984 (1)

1983 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

1981 (1)

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

1970 (1)

D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970).
[CrossRef]

Boyd, R. W.

M. T. Gruneisen, K. R. MacDonald, R. W. Boyd, J. Opt. Soc. Am. B 5, 123 (1988); M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, Phys. Rev. A 40, 3464 (1989).
[CrossRef] [PubMed]

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

Ducloy, M.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Firth, W. J.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970).
[CrossRef]

Gruneisen, M. T.

Grynberg, G.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Harter, D. J.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

Hesselink, L.

J. Pender, L. Hesselink, IEEE J. Quantum Electron. 25, 395 (1989); J. Opt. Soc. Am. B 7, 1361 (1990).
[CrossRef]

Khyzniak, A.

Khyzniak, A. I.

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

Kirilenko, E. K.

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

Kondilenko, V.

Kucherov, Yu.

Le Bihan, E.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Le Boiteux, S.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Leite, J. R. R.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Lesnik, S.

Lesnik, S. A.

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

MacDonald, K. R.

Markov, V. B.

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

Narum, P.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

Odoulov, S.

Paré, C.

Pender, J.

J. Pender, L. Hesselink, IEEE J. Quantum Electron. 25, 395 (1989); J. Opt. Soc. Am. B 7, 1361 (1990).
[CrossRef]

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Optical Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 2.

Raymer, M. G.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Optical Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 2.

Simoneau, P.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

Soskin, M.

Verkerk, P.

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Optical Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 2.

Appl. Phys. Lett. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 42, 919 (1983); Z. Zhang, G. Hu, X. Wu, S. Zhang, P. Ye, Opt. Commun. 69, 66 (1988); G. Hu, Z. Zhang, Y. Jiang, P. Ye, Opt. Commun. 71, 202 (1989); D. Statman, B. Liby, J. Opt. Soc. Am. B 6, 1884 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Pender, L. Hesselink, IEEE J. Quantum Electron. 25, 395 (1989); J. Opt. Soc. Am. B 7, 1361 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

Opt. Commun. (2)

G. Grynberg, E. Le Bihan, P. Verkerk, P. Simoneau, J. R. R. Leite, S. Le Boiteux, M. Ducloy, Opt. Commun. 67, 363 (1988).
[CrossRef]

E. K. Kirilenko, S. A. Lesnik, V. B. Markov, A. I. Khyzniak, Opt. Commun. 60, 9 (1986).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981); D. J. Harter, R. W. Boyd, Opt. Lett. 7, 491 (1982); R. W. Boyd, D. J. Harter, Appl. Phys. B 29, 163 (1982); A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef] [PubMed]

D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970).
[CrossRef]

Other (2)

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Optical Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 2.

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

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

Schematic of the experimental configuration.

Fig. 2
Fig. 2

Photograph of the TBE conical emission as observed on a screen located 2 m from the atomic sodium vapor cell. For this photograph the laser was tuned to the red side of the D2 line by 40 GHz.

Fig. 3
Fig. 3

Photograph of TBE conical emission when three beams are applied. The three possible pairings of the applied beams lead to the generation of three rings of different diameters.

Fig. 4
Fig. 4

Illustration of the phase-matching condition k1 + k2 = k3 + k4 for TBE conical emission, where k1 and k2 are the wave vectors of the applied waves and k3 and k4 are the wave vectors of the generated waves.

Equations (16)

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

P NL = 3 χ ( 3 ) E 2 E ,
E ( r ) = j = 1 4 A j ( r ) exp ( i k j · r ) ,             k j = ω / c ,
P 3 = 6 χ ( 3 ) A 1 A 2 A 4 * exp [ i ( k 1 + k 2 - k 3 - k 4 ) · r ] ,
P 4 = 6 χ ( 3 ) A 1 A 2 A 3 * exp [ i ( k 1 + k 2 - k 3 - k 4 ) · r ] .
k 1 = k x x ^ + k z z ^ ,             k 2 = - k x x ^ + k z z ^ ,
k j = k j x x ^ + k j y y ^ + k j z z ^
k 3 x 2 + k 3 y 2 = k 4 x 2 + k 4 y 2 = k x 2 ,
k 3 z = k 4 z = k z ,
k 3 x = - k 4 x ,             k 3 y = - k 4 y .
d A 3 d z = i 2 β ( A 1 2 + A 2 2 ) A 3 + i 2 β A 1 A 2 A 4 * ,
d A 4 * d z = - i 2 β ( A 1 2 + A 2 2 ) A 4 * - i 2 β A 1 * A 2 * A 3 ,
A 1 ( z ) = A 1 ( 0 ) exp [ i β ( A 1 2 + 2 A 2 2 ) z ] ,
A 2 ( z ) = A 2 ( 0 ) exp [ i β ( 2 A 1 2 + A 2 2 ) z ] .
A j ( z ) = B j exp ( G - z ) + C j exp ( G + z )             for j = 3 and 4 ,
G ± = i 3 π c β ( I 1 + I 2 ) ± π c β ( 14 I 1 I 2 - I 1 2 - I 2 2 ) 1 / 2 ,
I j ( z ) = C j 2 exp ( g I z )             for j = 3 and 4 ,

Metrics