Abstract

We present a simple yet highly sensitive single-beam experimental technique for the determination of both the sign and magnitude of n2. The sample is moved along the z direction of a focused Gaussian beam while the repetitively pulsed laser energy is held fixed. The resultant plot of transmittance through an aperture in the far field yields a dispersion-shaped curve from which n2 is easily calculated. A transmittance change of 1% corresponds to a phase distortion of ≃ λ/250. We demonstrate this method on several materials using both CO2 and Nd:YAG laser pulses.

© 1989 Optical Society of America

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References

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  1. M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).
  2. M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
    [CrossRef]
  3. S. R. Friberg, P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
    [CrossRef]
  4. R. Adair, L. L. Chase, S. A. Payne, J. Opt. Soc. Am. B 4, 875 (1987).
    [CrossRef]
  5. A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
    [CrossRef]
  6. W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
    [CrossRef]
  7. W. E. Williams, M. J. Soileau, E. W. Van Stryland, presented at the Fifteenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.
  8. J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
    [CrossRef]
  9. T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
    [CrossRef]
  10. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  11. D. Weaire, B. S. Wherrett, D. A. B. Miller, S. D. Smith, Opt. Lett. 4, 331 (1979).
    [CrossRef] [PubMed]
  12. J. N. Hayes, Appl. Opt. 11, 455 (1972).
    [CrossRef] [PubMed]
  13. V. Raman, K. S. Venkataraman, Proc. R. Soc. London Ser. A 171, 137 (1939).
    [CrossRef]

1987 (2)

S. R. Friberg, P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

R. Adair, L. L. Chase, S. A. Payne, J. Opt. Soc. Am. B 4, 875 (1987).
[CrossRef]

1984 (1)

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

1982 (1)

J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
[CrossRef]

1979 (1)

1978 (1)

M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).

1975 (1)

M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
[CrossRef]

1973 (1)

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

1972 (1)

1939 (1)

V. Raman, K. S. Venkataraman, Proc. R. Soc. London Ser. A 171, 137 (1939).
[CrossRef]

Adair, R.

Boggess, T. F.

T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
[CrossRef]

Boyd, I. W.

T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
[CrossRef]

Carman, R. L.

M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
[CrossRef]

Chase, L. L.

Friberg, S. R.

S. R. Friberg, P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Hayes, J. N.

Hill, J. R.

J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
[CrossRef]

Milam, D.

M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).

Miller, A.

J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
[CrossRef]

Miller, D. A. B.

Moran, M. J.

M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
[CrossRef]

Moss, S. C.

T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
[CrossRef]

Owyoung, A.

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

Parry, G.

J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
[CrossRef]

Payne, S. A.

Raman, V.

V. Raman, K. S. Venkataraman, Proc. R. Soc. London Ser. A 171, 137 (1939).
[CrossRef]

She, C. Y.

M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
[CrossRef]

Smirl, A. L.

T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
[CrossRef]

Smith, P. W.

S. R. Friberg, P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

Smith, S. D.

Smith, W. L.

M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).

Soileau, M. J.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, presented at the Fifteenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Van Stryland, E. W.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, presented at the Fifteenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Venkataraman, K. S.

V. Raman, K. S. Venkataraman, Proc. R. Soc. London Ser. A 171, 137 (1939).
[CrossRef]

Weaire, D.

Weber, M. J.

M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).

Wherrett, B. S.

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, presented at the Fifteenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Appl. Opt. (1)

IEEE J. Quantum Electron. (3)

M. J. Moran, C. Y. She, R. L. Carman, IEEE J. Quantum Electron. QE-11, 259 (1975).
[CrossRef]

S. R. Friberg, P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[CrossRef]

A. Owyoung, IEEE J. Quantum Electron. QE-9, 1064 (1973).
[CrossRef]

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

Opt. Commun. (2)

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

J. R. Hill, G. Parry, A. Miller, Opt. Commun. 43, 151 (1982).
[CrossRef]

Opt. Eng. (1)

M. J. Weber, D. Milam, W. L. Smith, Opt. Eng. 17, 463 (1978).

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

V. Raman, K. S. Venkataraman, Proc. R. Soc. London Ser. A 171, 137 (1939).
[CrossRef]

Other (3)

T. F. Boggess, S. C. Moss, I. W. Boyd, A. L. Smirl, in Ultrafast Phenomena IV, D. H. Huston, K. B. Eisenthal, eds. (Springer-Verlag, New York, 1984), p. 202.
[CrossRef]

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

W. E. Williams, M. J. Soileau, E. W. Van Stryland, presented at the Fifteenth Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

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Figures (3)

Fig. 1
Fig. 1

Simple Z-scan experimental apparatus in which the transmittance ratio D2/D1 is recorded as a function of the sample position z. BS, Beam splitter.

Fig. 2
Fig. 2

Measured Z scan of a 1-mm-thick CS2 cell using 300-nsec pulses at λ = 10.6 μm indicating thermal self-defocusing. The solid curve is the calculated result with ΔΦ0 = −0.6.

Fig. 3
Fig. 3

Measured Z scan of a 2.5-mm-thick BaF2 sample using 27-psec (FWHM) pulses at λ = 0.532 μm indicating the self-focusing due to the electronic Kerr effect. The solid curve is the theoretical fit with ΔΦ0 = 0.085 corresponding to ≃λ/75 phase distortion.

Equations (10)

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n = n 0 + n 2 2 | E | 2 = n 0 + Δ n ,
| E ( r , z , t ) | = | E 0 ( t ) | w 0 w ( z ) exp [ r 2 w 2 ( z ) ] ,
d Δ ϕ d z = 2 π / λ Δ n and d | E | d z = α / 2  | E | ,
Δ ϕ ( r , z , t ) = Δ Φ 0 1 + z 2 / z 0 2 exp [ 2 r 2 w 2 ( z ) ] ,
Δ Φ 0 ( t ) = 2 π λ Δ n 0 ( t ) 1 e αL α ,
E ( r , z 1 , t ) = E ( r , z 1 , t ) exp ( αL / 2 ) exp [ i Δ ϕ ( r , z 1 , t ) ] .
T ( z , t ) = 0 r a | E a ( Δ Φ 0 , r , z , t ) | 2 r d r S 0 | E a ( 0 , r , z , t ) | 2 r d r ,
Δ T p υ p | Δ Φ 0 | for | Δ Φ 0 | π ,
Δ T p υ 0 . 405 | Δ Φ 0 | for | Δ Φ 0 | π .
Δ n 0 d n d T 0 . 5 F 0 α ρ C υ ,

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