Abstract

We demonstrate a method for determining the phase of the third-order susceptibility, χ(3), in the proximity of a Raman resonance. The measurements were based on the phenomenon of polarization beats, which was exploited in a time-delayed four-wave-mixing experiment with bichromatic beams. The phase dispersion of χ(3) was studied close to resonance with the 655.7-cm−1 vibrational mode of carbon disulfide.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982); Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
    [CrossRef] [PubMed]
  3. S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
    [CrossRef]
  4. J. Chesnoy, A. Mokhtari, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds., Vol. 48 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1988), p. 366.
    [CrossRef]
  5. N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
    [CrossRef]
  6. R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
    [CrossRef] [PubMed]
  7. T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
    [CrossRef]
  8. N. Morita, K. Torizuka, T. Yajima, J. Opt. Soc. Am. B 3, 548 (1986).
    [CrossRef]
  9. M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
    [CrossRef]
  10. K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
    [CrossRef] [PubMed]
  11. M. Muller, K. Wynne, J. D. W. Van Voorst, J. Opt. Soc. Am. B 7, 1694 (1990).
    [CrossRef]
  12. K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
    [CrossRef] [PubMed]
  13. Z. Q. Huang, Y. J. Xie, G. L. Huang, H. S. Kwok, Opt. Lett. 15, 501 (1990).
    [CrossRef] [PubMed]
  14. D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
    [CrossRef] [PubMed]
  15. J. E. Rothenberg, D. Grischkowsky, Opt. Lett. 10, 22 (1985).
    [CrossRef] [PubMed]
  16. D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
    [CrossRef] [PubMed]
  17. V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).
  18. L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
    [CrossRef]
  19. H. Ma, A. S. L. Gomes, C. B. de Araújo, Opt. Lett. 16, 630 (1991).
    [CrossRef] [PubMed]
  20. H. Ma, A. S. L. Gomes, C. B. de Araújo, “Measurements of optical thickness by polarization beats interferometry,” Opt. Commun. (to be published).
  21. R. T. Lynch, H. Lotem, Phys. Rev. Lett. 37, 334 (1976).
    [CrossRef]

1991 (1)

1990 (4)

L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
[CrossRef]

M. Muller, K. Wynne, J. D. W. Van Voorst, J. Opt. Soc. Am. B 7, 1694 (1990).
[CrossRef]

K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
[CrossRef] [PubMed]

Z. Q. Huang, Y. J. Xie, G. L. Huang, H. S. Kwok, Opt. Lett. 15, 501 (1990).
[CrossRef] [PubMed]

1989 (2)

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
[CrossRef] [PubMed]

1988 (3)

D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
[CrossRef]

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

1986 (3)

N. Morita, K. Torizuka, T. Yajima, J. Opt. Soc. Am. B 3, 548 (1986).
[CrossRef]

M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
[CrossRef] [PubMed]

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

1985 (3)

J. E. Rothenberg, D. Grischkowsky, Opt. Lett. 10, 22 (1985).
[CrossRef] [PubMed]

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
[CrossRef] [PubMed]

1984 (1)

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

1976 (1)

R. T. Lynch, H. Lotem, Phys. Rev. Lett. 37, 334 (1976).
[CrossRef]

Acioli, L. H.

L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
[CrossRef]

Albrecht, A. C.

M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
[CrossRef]

Beach, R.

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
[CrossRef] [PubMed]

Bogdanov, V. L.

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

Chesnoy, J.

J. Chesnoy, A. Mokhtari, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds., Vol. 48 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1988), p. 366.
[CrossRef]

de Araújo, C. B.

H. Ma, A. S. L. Gomes, C. B. de Araújo, Opt. Lett. 16, 630 (1991).
[CrossRef] [PubMed]

L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
[CrossRef]

H. Ma, A. S. L. Gomes, C. B. de Araújo, “Measurements of optical thickness by polarization beats interferometry,” Opt. Commun. (to be published).

de Silvestri, S.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

DeBeer, D.

D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
[CrossRef] [PubMed]

Dugan, M. A.

M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
[CrossRef]

Evdokimov, A. B.

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

Fainberg, B. D.

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

Fujimoto, J. G.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

Gamble, E. B.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

Gomes, A. S. L.

H. Ma, A. S. L. Gomes, C. B. de Araújo, Opt. Lett. 16, 630 (1991).
[CrossRef] [PubMed]

L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
[CrossRef]

H. Ma, A. S. L. Gomes, C. B. de Araújo, “Measurements of optical thickness by polarization beats interferometry,” Opt. Commun. (to be published).

Grischkowsky, D.

Hartmann, S. R.

D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
[CrossRef] [PubMed]

Hattori, T.

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

Huang, G. L.

Huang, Z. Q.

Ippen, E. P.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

Kobayashi, T.

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

Kurokawa, K.

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

Kwok, H. S.

Levenson, M. D.

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982); Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Lotem, H.

R. T. Lynch, H. Lotem, Phys. Rev. Lett. 37, 334 (1976).
[CrossRef]

Lumonskii, G. V.

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

Lynch, R. T.

R. T. Lynch, H. Lotem, Phys. Rev. Lett. 37, 334 (1976).
[CrossRef]

Ma, H.

H. Ma, A. S. L. Gomes, C. B. de Araújo, Opt. Lett. 16, 630 (1991).
[CrossRef] [PubMed]

H. Ma, A. S. L. Gomes, C. B. de Araújo, “Measurements of optical thickness by polarization beats interferometry,” Opt. Commun. (to be published).

Melinger, J. S.

M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
[CrossRef]

Mokhtari, A.

J. Chesnoy, A. Mokhtari, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds., Vol. 48 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1988), p. 366.
[CrossRef]

Morita, N.

Muller, M.

K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
[CrossRef] [PubMed]

M. Muller, K. Wynne, J. D. W. Van Voorst, J. Opt. Soc. Am. B 7, 1694 (1990).
[CrossRef]

K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
[CrossRef] [PubMed]

Nelson, K. A.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

Rosker, M. J.

M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
[CrossRef] [PubMed]

Rothenberg, J. E.

Tang, C. L.

M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
[CrossRef] [PubMed]

Terasaki, A.

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

Torizuka, K.

Usadi, E.

D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

Van Voorst, J. D. W.

M. Muller, K. Wynne, J. D. W. Van Voorst, J. Opt. Soc. Am. B 7, 1694 (1990).
[CrossRef]

K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
[CrossRef] [PubMed]

Van Wagenen, L. G.

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

Voorst, J. D. W.

K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
[CrossRef] [PubMed]

Williams, L. R.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

Wise, F. W.

M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
[CrossRef] [PubMed]

Wynne, K.

K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
[CrossRef] [PubMed]

M. Muller, K. Wynne, J. D. W. Van Voorst, J. Opt. Soc. Am. B 7, 1694 (1990).
[CrossRef]

K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
[CrossRef] [PubMed]

Xie, Y. J.

Yajima, T.

Appl. Phys. B (1)

T. Kobayashi, A. Terasaki, T. Hattori, K. Kurokawa, Appl. Phys. B 47, 107 (1988).
[CrossRef]

Chem. Phys. Lett. (2)

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, K. A. Nelson, Chem. Phys. Lett. 116, 146 (1985).
[CrossRef]

M. A. Dugan, J. S. Melinger, A. C. Albrecht, Chem. Phys. Lett. 147, 411 (1988).
[CrossRef]

Electron Lett. (1)

L. H. Acioli, A. S. L. Gomes, C. B. de Araújo, Electron Lett. 26, 92 (1990).
[CrossRef]

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

JETP Lett. (1)

V. L. Bogdanov, A. B. Evdokimov, G. V. Lumonskii, B. D. Fainberg, JETP Lett. 49, 157 (1989).

Opt. Lett. (3)

Phys. Rev. A (3)

K. Wynne, M. Muller, J. D. W. Voorst, Phys. Rev. A 41, 6361 (1990).
[CrossRef] [PubMed]

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

R. Beach, D. DeBeer, S. R. Hartmann, Phys. Rev. A 32, 3467 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

M. J. Rosker, F. W. Wise, C. L. Tang, Phys. Rev. Lett. 57, 321 (1986).
[CrossRef] [PubMed]

K. Wynne, M. Muller, J. D. W. Van Voorst, Phys. Rev. Lett. 62, 3031 (1989).
[CrossRef] [PubMed]

D. DeBeer, E. Usadi, S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

D. DeBeer, L. G. Van Wagenen, R. Beach, S. R. Hartmann, Phys. Rev. Lett. 56, 1128 (1986).
[CrossRef] [PubMed]

R. T. Lynch, H. Lotem, Phys. Rev. Lett. 37, 334 (1976).
[CrossRef]

Other (3)

H. Ma, A. S. L. Gomes, C. B. de Araújo, “Measurements of optical thickness by polarization beats interferometry,” Opt. Commun. (to be published).

M. D. Levenson, Introduction to Nonlinear Laser Spectroscopy (Academic, New York, 1982); Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

J. Chesnoy, A. Mokhtari, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds., Vol. 48 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1988), p. 366.
[CrossRef]

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

Three-dimensional beam geometry used in the experiments. The intersection angles between the beams are ~2°.

Fig. 2
Fig. 2

Raman-enhanced four-wave-mixing spectrum and theoretical line shape associated with the 655.7-cm−1 Raman mode of CS2.

Fig. 3
Fig. 3

Recorded modulated diffracted signal for |ω2ω3| = 655.7 cm−1 as a function of the time delay between the two incident bichromatic beams.

Fig. 4
Fig. 4

Phase dispersion of the third-order susceptibility of CS2 as a function of the Raman frequency detuning.

Equations (7)

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

P A ( 3 ) ( ω 3 ) = χ ( 3 ) ( ω 3 , ω 1 - ω 1 , ω 3 ) E 1 E 1 * E 3 × exp i [ k 1 - k 1 + k 3 ] · r - ω 1 τ + ω 3 t + θ 3 ] ,
P B ( 3 ) ( ω 3 ) = χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) E 2 E 2 * E 3 × exp i [ ( k 2 - k 2 + k 3 ) · r - ω 2 τ + ω 3 t + θ 3 ] ,
S ( + ) { a 2 + b 2 + 2 a b × cos [ Δ k · r + ( ω 1 - ω 2 ) τ + ϕ ] } ,
a 2 = χ ( 3 ) ( ω 3 , ω 1 , - ω 1 , ω 3 ) 2 I 1 2 , b 2 = χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) 2 I 2 2 ,
ϕ = arctan [ Im χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) Re χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) ] - arctan [ Im χ ( 3 ) ( ω 3 , ω 1 , - ω 1 , ω 3 ) Re χ ( 3 ) ( ω 3 , ω 1 , - ω 1 , ω 3 ) ] .
χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) = [ χ NR ( 3 ) + χ TPA ( 3 ) ] + R ω R - ( ω 2 - ω 3 ) + i Γ R ,
ϕ = arctan [ Im χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) Re χ ( 3 ) ( ω 3 , ω 2 , - ω 2 , ω 3 ) ] .

Metrics