Abstract

Z-scan measurement with a slit instead of a circular aperture is proposed and analyzed for an astigmatic Gaussian beam. This new technique can accurately determine not only the nonlinear refractive index but also the ellipticity and positions of xy foci of the astigmatic beam.

© 2000 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. V. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  2. S. M. Mian, B. Taheri, and J. P. Wicksted, “Effect of beam ellipticity on Z-scan measurements,” J. Opt. Soc. Am. B 13, 856–863 (1996).
    [CrossRef]

1996 (1)

1990 (1)

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

Hagan, D. J.

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

Mian, S. M.

Said, A. A.

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

Sheik-Bahae, M.

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

Stryland, E. W. V.

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

Taheri, B.

Wei, T.-H.

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

Wicksted, J. P.

IEEE J. Quantum Electron. (1)

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

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

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Figures (8)

Fig. 1
Fig. 1

(a) Z-scan traces with focused beam radii of w0x=20 µm and w0y=10 µm. Traces Tx and Ty were measured with slits perpendicular to the x and y directions, respectively. Trace Tc was measured with a circular aperture. (b) Z-scan traces with focused beam radii of w0x=40 µm and w0y=10 µm.

Fig. 2
Fig. 2

Ellipticity versus peak-to-valley difference ratio.

Fig. 3
Fig. 3

Ratio between dominant peak-to-valley difference and nonlinear phase change versus ellipticity.

Fig. 4
Fig. 4

Z-scan traces with focused beam radii of w0x=40 µm and w0y=10 µm located at zx=2000 µm and zy=0 µm, respectively.

Fig. 5
Fig. 5

Z-scan traces with focused beam radii of w0x=20 µm and w0y=10 µm located at zx=2000 µm and zy=0 µm, respectively.

Fig. 6
Fig. 6

Z-scan traces with focused beam radii of w0x=20 µm and w0y=10 µm located at zx=1000 µm and zy=0 µm, respectively.

Fig. 7
Fig. 7

Z-scan traces with focused beam radii of w0x=40 µm and w0y=10 µm located at zx=2000 µm and zy=0 µm, respectively.

Fig. 8
Fig. 8

Z-scan traces with two-photon absorption considered for focused beam radii of w0x=40 µm and w0y=10 µm located at zx=2000 µm and zy=0 µm, respectively.

Equations (10)

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Ea(x, y, z, t)
=E(0, 0, z, t)exp(-αL/2)
×m=0wm0x(z)wm0y(z)Wmx(z)wmy(z)1/2 exp[iηm(z)]×exp-ikx22qmx(z)-iky22qmy(z) [iΔϕ0(z, t)]mm!,
Ty(z)=-y0/2y0/2-|Ea(x, y, z, ΔΦ0)|2dxdy-y0/2y0/2-|Ea(x, y, z, 0)|2dxdy,
ξ=(0.398+0.662x-0.0375x2)S-k,
x=ΔTyΔTx,k=-0.0167+0.3194(S-0.0972)2+0.0162.
ΔTyΔΦ0=0.309-0.0804 exp-(ξ-1)0.472S-k,
k=-0.119+0.2594(S-0.957)2+0.0234.
Δxy=w0y2f(ξ),
f(ξ)=1.231-0.594ξ+0.494ξ2,

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