Abstract

We report on a method aimed at measuring both the real and imaginary parts of the third-order Kerr-type nonlinear-optical susceptibility of isotropic materials. It is based on Kerr ellipsometry in which analysis of the polarization state of transmitted light between a nearly crossed polarizer and an analyzer allows separation of pump-induced dichroism and birefringence. The method provides a natural measurement of nonlinear phase retardations in angle units, without any calibration procedure. By using a white-light continuum as a probe, this property is used to get a simultaneous measurement of the nonlinear dispersion in the whole visible spectrum. It is illustrated in tetramethylsilane, where stimulated Stokes and anti-Stokes Raman contributions to the nonlinearity are observed.

© 1991 Optical Society of America

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References

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  1. L. A. Lugiato, Contemp. Phys. 24, 333 (1983).
    [CrossRef]
  2. K. W. DeLong, G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
    [CrossRef]
  3. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
    [CrossRef] [PubMed]
  4. M. L. Shand, R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
    [CrossRef]
  5. J. M. Nunzi, E. Charra, Appl. Phys. Lett. 59, 13 (1991).
    [CrossRef]
  6. P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
    [CrossRef]
  7. S. M. Saltiel, B. Van Wonterghem, P. M. Rentzepis, Opt. Lett. 14, 183 (1989).
    [CrossRef] [PubMed]
  8. H. Ma, L. H. Acioli, A. S. L. Gomes, C. B. de Araúdjo, Opt. Lett. 16, 630 (1991).
    [CrossRef] [PubMed]
  9. M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 15, 192 (1969).
    [CrossRef]
  10. M. D. Levenson, G. L. Eesley, Appl. Phys. 19, 1 (1979).
    [CrossRef]
  11. R. R. Alfano, The Supercontinum Laser Source (Springer-Verlag, Berlin, 1989).
  12. M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
    [CrossRef]
  13. P. P. Ho, R. R. Alfano, Phys. Rev. A 20, 2170 (1979).
    [CrossRef]
  14. D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
    [CrossRef]
  15. R. Deltheil, Erreurs et Moindres Carrés (Gauthiers-Villars, Paris, 1930), p. 104.
  16. B. Schrader, Raman Infrared Atlas of Organic Compounds (VCH, Weinheim, Germany, 1989).
  17. M. J. Colles, Opt. Commun. 1, 169 (1969).
    [CrossRef]
  18. D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
    [CrossRef]
  19. M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986), p. 202.

1991 (2)

1990 (1)

K. W. DeLong, G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

1989 (2)

1987 (1)

P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
[CrossRef]

1983 (2)

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

L. A. Lugiato, Contemp. Phys. 24, 333 (1983).
[CrossRef]

1981 (1)

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

1979 (2)

P. P. Ho, R. R. Alfano, Phys. Rev. A 20, 2170 (1979).
[CrossRef]

M. D. Levenson, G. L. Eesley, Appl. Phys. 19, 1 (1979).
[CrossRef]

1978 (1)

M. L. Shand, R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

1976 (1)

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

1969 (2)

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 15, 192 (1969).
[CrossRef]

M. J. Colles, Opt. Commun. 1, 169 (1969).
[CrossRef]

Acioli, L. H.

Alfano, R. R.

P. P. Ho, R. R. Alfano, Phys. Rev. A 20, 2170 (1979).
[CrossRef]

R. R. Alfano, The Supercontinum Laser Source (Springer-Verlag, Berlin, 1989).

Chance, R. R.

M. L. Shand, R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

Charra, E.

J. M. Nunzi, E. Charra, Appl. Phys. Lett. 59, 13 (1991).
[CrossRef]

Colles, M. J.

M. J. Colles, Opt. Commun. 1, 169 (1969).
[CrossRef]

Cross, A. J.

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

de Araúdjo, C. B.

DeLong, K. W.

K. W. DeLong, G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Deltheil, R.

R. Deltheil, Erreurs et Moindres Carrés (Gauthiers-Villars, Paris, 1930), p. 104.

Duguay, M. A.

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 15, 192 (1969).
[CrossRef]

Eesley, G. L.

M. D. Levenson, G. L. Eesley, Appl. Phys. 19, 1 (1979).
[CrossRef]

Fleming, G. R.

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

Flytzanis, C.

P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
[CrossRef]

Gomes, A. S. L.

Gulbinas, V.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Hansen, J. W.

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 15, 192 (1969).
[CrossRef]

Heiman, D.

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Hellwarth, R. W.

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Ho, P. P.

P. P. Ho, R. R. Alfano, Phys. Rev. A 20, 2170 (1979).
[CrossRef]

Kabelka, V.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Levenson, M. D.

M. D. Levenson, G. L. Eesley, Appl. Phys. 19, 1 (1979).
[CrossRef]

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Lugiato, L. A.

L. A. Lugiato, Contemp. Phys. 24, 333 (1983).
[CrossRef]

Ma, H.

Malyshev, V. I.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Martin, G.

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Masalov, A. V.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

McDonald, D. B.

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

Nunzi, J. M.

J. M. Nunzi, E. Charra, Appl. Phys. Lett. 59, 13 (1991).
[CrossRef]

Rentzepis, P. M.

Ricard, D.

P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
[CrossRef]

Roussignol, P.

P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
[CrossRef]

Said, A. A.

Saltiel, S. M.

Schrader, B.

B. Schrader, Raman Infrared Atlas of Organic Compounds (VCH, Weinheim, Germany, 1989).

Schubert, M.

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986), p. 202.

Shand, M. L.

M. L. Shand, R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

Sheik-Bahae, M.

Stegeman, G. I.

K. W. DeLong, G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Syrus, V.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Van Stryland, E. W.

Van Wonterghem, B.

Vasil’eva, M. A.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Vishchakas, J.

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

Waldeck, D.

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

Wilhelmi, B.

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986), p. 202.

Appl. Phys. (1)

M. D. Levenson, G. L. Eesley, Appl. Phys. 19, 1 (1979).
[CrossRef]

Appl. Phys. A (1)

P. Roussignol, D. Ricard, C. Flytzanis, Appl. Phys. A 44, 285 (1987).
[CrossRef]

Appl. Phys. Lett. (3)

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 15, 192 (1969).
[CrossRef]

K. W. DeLong, G. I. Stegeman, Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

J. M. Nunzi, E. Charra, Appl. Phys. Lett. 59, 13 (1991).
[CrossRef]

Contemp. Phys. (1)

L. A. Lugiato, Contemp. Phys. 24, 333 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. A. Vasil’eva, J. Vishchakas, V. Gulbinas, V. I. Malyshev, A. V. Masalov, V. Kabelka, V. Syrus, IEEE J. Quantum Electron. 19, 724 (1983).
[CrossRef]

J. Chem. Phys. (2)

D. Waldeck, A. J. Cross, D. B. McDonald, G. R. Fleming, J. Chem. Phys. 74, 3381 (1981); G. S. Beddard, M. J. Westby, Chem. Phys. 57, 121 (1981).
[CrossRef]

M. L. Shand, R. R. Chance, J. Chem. Phys. 69, 4482 (1978).
[CrossRef]

Opt. Commun. (1)

M. J. Colles, Opt. Commun. 1, 169 (1969).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

P. P. Ho, R. R. Alfano, Phys. Rev. A 20, 2170 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

D. Heiman, R. W. Hellwarth, M. D. Levenson, G. Martin, Phys. Rev. Lett. 36, 189 (1976).
[CrossRef]

Other (4)

M. Schubert, B. Wilhelmi, Nonlinear Optics and Quantum Electronics (Wiley, New York, 1986), p. 202.

R. Deltheil, Erreurs et Moindres Carrés (Gauthiers-Villars, Paris, 1930), p. 104.

B. Schrader, Raman Infrared Atlas of Organic Compounds (VCH, Weinheim, Germany, 1989).

R. R. Alfano, The Supercontinum Laser Source (Springer-Verlag, Berlin, 1989).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for Kerr ellipsometry. The inset depicts polarization directions of the pump and the gated probe beams. OMA, optical multichannel analyzer.

Fig. 2
Fig. 2

Typical signal intensity dependence on the analyzer angle. Data correspond to a 627-nm probe beam transmitted using a quarter-wave plate with (●) and without (○) the chopped pump. The solid and dashed curves are fits calculated with Eq. (6).

Fig. 3
Fig. 3

Instantaneous phase retardations induced by 250-MW/cm2, 532-nm pump in 1 mm of TMS. Real and imaginary parts are measured with and without the quarter-wave plate, respectively. The pump-saturated zone appears as a peak in the error level.

Equations (7)

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E s = E in exp ( i φ 0 ) ( u cos δ φ + i v sin δ φ ) ,
( n x + n y ) ( n x - n y ) = 3 2 [ χ x x x x ( 3 ) ( ω ; ω p , - ω p , ω ) ] - χ y x x y ( 3 ) ( ω ; ω p , - ω p , ω ) ] E p E p * .
I t = 1 2 I in exp ( - 2 φ 0 ) [ cosh ( 2 δ φ ) - cos ( 2 δ φ ) cos ( 2 α ) - sinh ( 2 δ φ ) sin ( 2 α ) ] ,
I t = I in exp ( - 2 φ 0 ) [ ( δ φ - α ) 2 + ( δ φ ) 2 ] .
T = ( δ φ - α ) 2 + δ φ 2 + ( δ φ 2 - δ φ 2 ) ,
I t = I in exp ( - 2 φ 0 ) [ ( δ φ - α ) 2 + ( δ φ ) 2 ] .
γ ( ω p , - ω p , ω ) = 1 6 3 ± v [ 1 ω v g ± ω ω p ± i Γ v × ( e μ g e μ e v ω e g ± ω + μ v e μ e g ω e g ω p ) 2 ] ,

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