Abstract

A detailed study on yellow conical emission observed in dense sodium vapor following near-resonant one-photon excitation of the Na 42P levels was performed. The origins of conical emission are suggested to be due to Raman resonant four-wave parametric mixing processes. In order to describe spectral and spatial features of off-axis emission, we introduce self-phase modulation and induced-phase modulation as important additional nonlinear processes, explaining the nonmonotonic detuning of the wavelength of the conical radiation with the exiting laser wavelength in the vicinity of resonance transitions. The spatial evolution of emission generated via four-wave mixing is modeled by solving the two-dimensional nonlinear Schrödinger equation describing the spatial evolution of light beams in a nonlinear media. Experimental and theoretical results are presented and discussed.

© 1998 Optical Society of America

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  1. Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).
  2. D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1981).
    [CrossRef]
  3. R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
    [CrossRef]
  4. W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
    [CrossRef]
  5. Y. Shevy and M. Rosenbluh, J. Opt. Soc. Am. B 5, 116 (1988).
    [CrossRef]
  6. U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
    [CrossRef]
  7. A. C. Tam, Phys. Rev. A 19, 1971 (1979).
    [CrossRef]
  8. E. A. Chauchard and Y. H. Meyer, Opt. Commun. 52, 141 (1984).
    [CrossRef]
  9. M. E. Cernshaw and C. D. Cantrell, Phys. Rev. A 39, 126 (1989).
    [CrossRef]
  10. N. V. Lugovoi and A. M. Prokhorov, Sov. Phys. JETP 42, 42 (1975).
  11. I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
    [CrossRef]
  12. L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
    [CrossRef] [PubMed]
  13. L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
    [CrossRef] [PubMed]
  14. M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
    [CrossRef]
  15. J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
    [CrossRef] [PubMed]
  16. Y. Silverberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef]
  17. A. Dreischuh, U. Reiter-Domiaty, D. Gruber, L. Windholz, and S. Dinev, Appl. Phys. B (to be published).
  18. P. Sorokin and J. Wynne, in Nonlinear Infrared Generation, Y. R. Shen, ed., Vol. 16 of Topics of Applied Physics (Springer, Berlin, 1977), p. 160.
  19. J. F. Raintjes, ed., Nonlinear Optical Parametric Processes in Gases and Liquids (Academic, Boston, Mass., 1988).
  20. R. Alfano and P. Ho, “Self-, cross-, and induced-phase modulation of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. QE-24, 351 (1988).
    [CrossRef]
  21. R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470 (1973).
    [CrossRef]
  22. S. Dinev and A. Dreischuh, “Sum-frequency generation in the xuv,” Opt. Quantum Electron. 23, 91 (1991).
    [CrossRef]
  23. Y. Prior, “A complete expression for the third-order susceptibility: perturbative and diagrammatical approach,” IEEE J. Quantum Electron. QE-20, 37 (1984).
    [CrossRef]
  24. R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
    [CrossRef]
  25. G. Yang and Y. R. Chen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510 (1984).
    [CrossRef] [PubMed]
  26. R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
    [CrossRef]

1994 (1)

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

1993 (1)

W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
[CrossRef]

1992 (2)

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

1991 (1)

S. Dinev and A. Dreischuh, “Sum-frequency generation in the xuv,” Opt. Quantum Electron. 23, 91 (1991).
[CrossRef]

1990 (3)

R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
[CrossRef]

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Y. Silverberg, Opt. Lett. 15, 1282 (1990).
[CrossRef]

1989 (1)

M. E. Cernshaw and C. D. Cantrell, Phys. Rev. A 39, 126 (1989).
[CrossRef]

1988 (2)

R. Alfano and P. Ho, “Self-, cross-, and induced-phase modulation of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. QE-24, 351 (1988).
[CrossRef]

Y. Shevy and M. Rosenbluh, J. Opt. Soc. Am. B 5, 116 (1988).
[CrossRef]

1986 (1)

I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
[CrossRef]

1984 (4)

G. Yang and Y. R. Chen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510 (1984).
[CrossRef] [PubMed]

Y. Prior, “A complete expression for the third-order susceptibility: perturbative and diagrammatical approach,” IEEE J. Quantum Electron. QE-20, 37 (1984).
[CrossRef]

E. A. Chauchard and Y. H. Meyer, Opt. Commun. 52, 141 (1984).
[CrossRef]

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

1981 (2)

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1981).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

1979 (1)

A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef]

1975 (1)

N. V. Lugovoi and A. M. Prokhorov, Sov. Phys. JETP 42, 42 (1975).

1974 (1)

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
[CrossRef]

1973 (1)

R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470 (1973).
[CrossRef]

1970 (1)

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

Alfano, R.

R. Alfano and P. Ho, “Self-, cross-, and induced-phase modulation of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. QE-24, 351 (1988).
[CrossRef]

Allegrini, M.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Boyd, R. W.

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1981).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

Cantrell, C. D.

M. E. Cernshaw and C. D. Cantrell, Phys. Rev. A 39, 126 (1989).
[CrossRef]

Cernshaw, M. E.

M. E. Cernshaw and C. D. Cantrell, Phys. Rev. A 39, 126 (1989).
[CrossRef]

Chalupczak, W.

W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
[CrossRef]

Chauchard, E. A.

E. A. Chauchard and Y. H. Meyer, Opt. Commun. 52, 141 (1984).
[CrossRef]

Chen, Y. R.

Chernobrod, B. M.

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

Cooper, J.

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

de Fillipo, G.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Dinev, S.

S. Dinev and A. Dreischuh, “Sum-frequency generation in the xuv,” Opt. Quantum Electron. 23, 91 (1991).
[CrossRef]

Dinev, S. G.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Domiaty, U.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Dreischuh, A.

S. Dinev and A. Dreischuh, “Sum-frequency generation in the xuv,” Opt. Quantum Electron. 23, 91 (1991).
[CrossRef]

Eckardt, R. C.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
[CrossRef]

Erez, G.

I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
[CrossRef]

Fuso, F.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Gawlik, W.

W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
[CrossRef]

Gibbs, H. M.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Golub, I.

I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
[CrossRef]

Grantham, J. W.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Gruber, D.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Harris, S. E.

R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470 (1973).
[CrossRef]

Harter, D. J.

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1981).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

Ho, P.

R. Alfano and P. Ho, “Self-, cross-, and induced-phase modulation of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. QE-24, 351 (1988).
[CrossRef]

Khitrova, G.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Kirin, Y. M.

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

LeBerre, M.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
[CrossRef]

Lugovoi, N. V.

N. V. Lugovoi and A. M. Prokhorov, Sov. Phys. JETP 42, 42 (1975).

McMichael, I.

R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
[CrossRef]

Meyer, Y. H.

E. A. Chauchard and Y. H. Meyer, Opt. Commun. 52, 141 (1984).
[CrossRef]

Miles, R. B.

R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470 (1973).
[CrossRef]

Mostowski, J.

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

Naurum, P.

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

Peyghambarian, N.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Prior, Y.

Y. Prior, “A complete expression for the third-order susceptibility: perturbative and diagrammatical approach,” IEEE J. Quantum Electron. QE-20, 37 (1984).
[CrossRef]

Prokhorov, A. M.

N. V. Lugovoi and A. M. Prokhorov, Sov. Phys. JETP 42, 42 (1975).

Rautian, S. G.

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

Raymer, M. G.

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

Reintjes, J.

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
[CrossRef]

Ressayre, E.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Rinkleff, R. H.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Rosenbluh, M.

Rushford, M. C.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Saxena, R.

R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
[CrossRef]

Semenov, A. E.

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

Shevy, Y.

Shuker, R.

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
[CrossRef]

Silverberg, Y.

Tai, K.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Tallet, A.

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

Tam, A. C.

A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef]

Valley, J. F.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Windholz, L.

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

Xu, J.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Yang, G.

Yeh, P.

R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
[CrossRef]

You, L.

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

Zachorowski, J.

W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
[CrossRef]

Appl. Phys. B (2)

U. Domiaty, D. Gruber, L. Windholz, S. G. Dinev, M. Allegrini, G. de Fillipo, F. Fuso, and R. H. Rinkleff, Appl. Phys. B 59, 525 (1994).
[CrossRef]

R. Saxena, I. McMichael, and P. Yeh, “Dynamics of refractive-index changes and two-beam coupling in resonant media,” Appl. Phys. B 51, 243 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

R. H. Lehmberg, J. Reintjes, and R. C. Eckardt, “Two-photon resonantly enhanced self-defocusing in Cs vapor at 1.06 mm,” Appl. Phys. Lett. 25, 374 (1974).
[CrossRef]

IEEE J. Quantum Electron. (3)

Y. Prior, “A complete expression for the third-order susceptibility: perturbative and diagrammatical approach,” IEEE J. Quantum Electron. QE-20, 37 (1984).
[CrossRef]

R. Alfano and P. Ho, “Self-, cross-, and induced-phase modulation of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. QE-24, 351 (1988).
[CrossRef]

R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

M. LeBerre, E. Ressayre, A. Tallet, K. Tai, H. M. Gibbs, M. C. Rushford, and N. Peyghambarian, J. Opt. Soc. Am. 1, 591 (1984).
[CrossRef]

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

JETP Lett. (1)

Y. M. Kirin, S. G. Rautian, A. E. Semenov, and B. M. Chernobrod, JETP Lett. 11, 226 (1970).

Opt. Commun. (3)

W. Chalupczak, W. Gawlik, and J. Zachorowski, Opt. Commun. 99, 49 (1993).
[CrossRef]

E. A. Chauchard and Y. H. Meyer, Opt. Commun. 52, 141 (1984).
[CrossRef]

I. Golub, R. Shuker, and G. Erez, Opt. Commun. 57, 143 (1986).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

S. Dinev and A. Dreischuh, “Sum-frequency generation in the xuv,” Opt. Quantum Electron. 23, 91 (1991).
[CrossRef]

Phys. Rev. A (6)

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2925 (1992).
[CrossRef] [PubMed]

L. You, J. Mostowski, J. Cooper, and R. Shuker, Phys. Rev. A 46, 2903 (1992).
[CrossRef] [PubMed]

M. E. Cernshaw and C. D. Cantrell, Phys. Rev. A 39, 126 (1989).
[CrossRef]

A. C. Tam, Phys. Rev. A 19, 1971 (1979).
[CrossRef]

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1981).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Naurum, and D. J. Harter, Phys. Rev. A 24, 441 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Grantham, and J. Xu, Phys. Rev. Lett. 64, 2362 (1990).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

N. V. Lugovoi and A. M. Prokhorov, Sov. Phys. JETP 42, 42 (1975).

Other (3)

A. Dreischuh, U. Reiter-Domiaty, D. Gruber, L. Windholz, and S. Dinev, Appl. Phys. B (to be published).

P. Sorokin and J. Wynne, in Nonlinear Infrared Generation, Y. R. Shen, ed., Vol. 16 of Topics of Applied Physics (Springer, Berlin, 1977), p. 160.

J. F. Raintjes, ed., Nonlinear Optical Parametric Processes in Gases and Liquids (Academic, Boston, Mass., 1988).

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Figures (11)

Fig. 1
Fig. 1

Simplified Na energy-level diagram with a scheme of the FWPM processes observed.

Fig. 2
Fig. 2

Typical spectra of the yellow emission around the Na D lines for different values of the exciting laser wavelength λL (a) 329.05-nm, (b) 330.50-nm, (c) 329.90-nm, and (d) 330.10-nm.

Fig. 3
Fig. 3

Third-order nonlinear susceptibility for laser SPM versus wavelength (horizontal solid and vertical dashed lines indicate the wavelengths, at which the susceptibility changes its sign).

Fig. 4
Fig. 4

Third-order nonlinear susceptibility for IPM of the infrared emission (wavelength λIR=9140.96 nm) versus laser wavelength (the solid and dashed lines have the same meaning as those in Fig. 3).

Fig. 5
Fig. 5

Dispersion of the third-order nonlinear susceptibility for IPM of the yellow emission at a specific laser wavelength λL =330.298 nm. (The solid and dashed lines have the same meaning as those in Fig. 3).

Fig. 6
Fig. 6

Center-of-gravity wavelength of the conical emission versus the pump-laser wavelength retrieved from the experimental data. Circles indicate numerically obtained solutions of Eq. (5), based on the χSPM(3) dispersion curves shown in Figs. 35.

Fig. 7
Fig. 7

Conical radiation half-angle in dependence of the laser wavelength (points indicate measured values, and the solid curve indicates calculation).

Fig. 8
Fig. 8

Dispersion of the third-order nonlinear susceptibility for SPM in the vicinity of the Na first fine-structure doublet. (The solid line indicates the sign-change of χSPM(3) and the dashed line indicates the Na D lines). The arrows denote the wavelengths λY, at which the numerical simulations shown in Figs. 911 are carried out.

Fig. 9
Fig. 9

Gray-scale patterns of the yellow conical emission recorded experimentally (a) at λL=329.65 nm (λY=590.3 nm) and (b) generated numerically.

Fig. 10
Fig. 10

Same as in Fig. 10 for λL=329.53 nm (λY =590.2 nm).

Fig. 11
Fig. 11

Simulation results for λL=329.825 nm (λY =590.0 nm): (a) nonlinear medium without fluctuations (the beam is focused in the center); (b) nonlinear heterogeneous medium (the symmetry in the picture is due to the symmetry in the perturbation).

Equations (15)

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

kL=kIR+kR+kY.
n(λi)=n0(λi)+n2SPM(λi)Ii+n2IPM(λi)Ij,i, j=1, 2;ij.
kNNL=kL{nSPMLIL+nIPML,IRIIR+nIPML,YIY},
kIRNL=kIR{nSPMIRIIR+nIPMIR,LIL+nIPMIR,RIR},
kRNL=kL{nSPMRIR+nIPMR,IRIIR+nIPMR,YIY},
kYNL=kL{nSPMYIY+nIPMY,RIR+nIPMY,LIL},
ΔkNL=kLNL-(kIRNL+kRNL+kYNL).
ΔkNL={kLnLSPM-kIRnIPMIR,L-kYnIPMY,L}IL.
ΔkNL(λL, λY, λIR)=0
λL-1χSPM(3)(λL)-λIR-1χIPM(3)(λIRλL)-λY-1χIPM(3)(λYλL)=0,
i Az+12LD 2x2+2y2A+sign[n2SPM(λY)]LNL |A|2A
=0,
LD=kr02,
LNL=(k|n2SPM|I)-1.
A=A1 exp-(r-R1)2r02+A2 exp-(r-R2)2r02exp(-t2)

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