Abstract

We report a theoretical study of the Z-scan technique by using quasi-one-dimensional slit beams for characterizing third-order optical nonlinearity. We verify that the sensitivity of this Z-scan scheme is roughly the same level as top-hat beams and is greatly higher than Gaussian beams by a factor of approximately 2.5. This scheme should have the capability to measure less than a λ/500 wave-front distortion at least. Numerical formulas obtained in theory allow direct estimation of nonlinear refraction and absorption coefficients from the normalized peak–valley transmittance difference measured. Some salient features are also discussed. This Z-scan scheme is also demonstrated experimentally.

© 2004 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  2. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. Marcano O., F. E. Hernandez, and A. D. Sena, “Two-color near-field eclipsing Z-scan technique for the determination of nonlinear refraction,” J. Opt. Soc. Am. B 14, 3363–3367 (1997).
    [CrossRef]
  6. W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
    [CrossRef]
  7. W. Zhao and P. Palffy-Muhoray, “Z-scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
    [CrossRef]
  8. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]
  9. H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
    [CrossRef]
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    [CrossRef]
  11. K. Y. Tseng, K. S. Wong, and G. K. L. Wong, “Femtosecond time-resolved Z-scan investigations of optical nonlinearities in ZnSe,” Opt. Lett. 21, 180–182 (1996).
    [CrossRef] [PubMed]
  12. S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian–Bessel beams,” Phys. Rev. A 56, R1103–R1106 (1997).
    [CrossRef]
  13. P. B. Chapple, J. Staromlynska, and R. G. McDuff, “Z-scan studies in the thin- and the thick-sample limits,” J. Opt. Soc. Am. B 11, 975–982 (1994).
    [CrossRef]
  14. R. E. Bridges, G. L. Fischer, and R. W. Boyd, “Z-scan measurement technique for non-Gaussian beams and arbitrary sample thicknesses,” Opt. Lett. 20, 1821–1823 (1995).
    [CrossRef] [PubMed]
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  16. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 457 and the related references.

1997 (2)

1996 (1)

1995 (2)

1994 (4)

1993 (1)

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

1992 (1)

1991 (1)

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1989 (1)

Boyd, R. W.

Bridges, R. E.

Burzler, J. M.

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian–Bessel beams,” Phys. Rev. A 56, R1103–R1106 (1997).
[CrossRef]

Castillo, J.

Chapple, P. B.

de Araujo, C. B.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

DeSalvo, R.

Fischer, G. L.

Gomes, A. S. L.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Hagan, D. J.

Hernandez, F. E.

Hughes, S.

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian–Bessel beams,” Phys. Rev. A 56, R1103–R1106 (1997).
[CrossRef]

Kershaw, S. V.

S. V. Kershaw, “Analysis of the EZ scan measurement technique,” J. Mod. Opt. 42, 1361–1366 (1995).
[CrossRef]

Kozich, V. P.

Ma, H.

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Marcano O., A.

McDuff, R. G.

Palffy-Muhoray, P.

W. Zhao and P. Palffy-Muhoray, “Z-scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef] [PubMed]

Sena, A. D.

Sheik-Bahae, M.

Staromlynska, J.

Tseng, K. Y.

Van Stryland, E. W.

Wang, J.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wong, G. K. L.

Wong, K. S.

Xia, T.

Zhao, W.

W. Zhao and P. Palffy-Muhoray, “Z-scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Appl. Phys. Lett. (3)

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Appl. Spectrosc. (1)

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Mod. Opt. (1)

S. V. Kershaw, “Analysis of the EZ scan measurement technique,” J. Mod. Opt. 42, 1361–1366 (1995).
[CrossRef]

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

Opt. Lett. (5)

Phys. Rev. A (1)

S. Hughes and J. M. Burzler, “Theory of Z-scan measurements using Gaussian–Bessel beams,” Phys. Rev. A 56, R1103–R1106 (1997).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, U.K., 1980), Sec. 8.8.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 457 and the related references.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the QODS Z-scan setup.

Fig. 2
Fig. 2

Z-scan traces with the QODS beams at four pairs of different values of S and ϕ0.

Fig. 3
Fig. 3

Asymmetric parameter A against S and ϕ0.

Fig. 4
Fig. 4

Tpv against S and ϕ0.

Fig. 5
Fig. 5

Tpv(tophat)/Tpv against S and ϕ0.

Fig. 6
Fig. 6

Z-scan traces with S=1 (solid curves) and with S1 (dashed curves) at different values of ϕ0 and ψ0.

Fig. 7
Fig. 7

Z-scan traces obtained from a CS2 sample. Solid curves, the theoretical fitting; circles, experimental points. (a) S=0.21 and (b) S=0.07.

Equations (10)

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

E(x; z)sin(πxD/fλ)πxD/fλexp(iπx2/λz)λz,
E(x; z=0)sin(πx/ω0)πx/ω0,
Re[χ(3)]=2n020cγ,
Im[χ(3)]=n020cβ/k,
Eout(x; z)=E(x; z)exp[iϕ0|E(x; z)|2],
Tpv(tophat)/Tpv=1.28673-0.79S0.79.
Tpv=1.67(1-S1.8)sin(0.48ϕ0).
Eout(x, z)=E(x, z)exp(-α0L/2)×[1+ψ0|E(x, z)|2]iϕ0/ψ0-1/2,
Tvdepth1=0.641[1-exp(-0.91ψ0)].
Tpv0=[0.546+1.124 exp(-0.585ψ0)]×sin[0.48ϕ0 sinh(1-0.1ψ0)].

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