Abstract

A cw-probe Z-scan technique was employed to measure the photoinduced index change in a photorefractive SBN:60 crystal. For this experiment a three-detector data-acquisition system was used to account for temporal changes in the laser. The effects of various beam parameters such as intensity, polarization, and wavelength were studied. A theoretical simulation of the Z scan based on a band-transport model of photorefractive-index variation was also developed. This model provides reasonable agreement with the experimental results.

© 2000 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearity using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  2. P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, Berlin, 1988, 1989), Vols. 61 and 62.
  3. M. Horowitz, R. Daisy, O. Werner, B. Fischer, “Large thermal nonlinearities and spatial self-phase modulation in Srx Ba1-xNb2O6 and BaTiO3 crystals,” Opt. Lett. 17, 475–477 (1992).
    [CrossRef] [PubMed]
  4. P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
    [CrossRef]
  5. R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
    [CrossRef]
  6. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. A 72, 46–51 (1982).
  7. D. Breitling, A. Siahmakoun, “Laser beam self-focusing and defocusing in a SBN:60,” Presented at the OSA Annual Meeting, Rochester, N.Y., 20–24 Oct. 1996 (Optical Society of America, Washington, D.C.).
  8. D. Breitling, “An investigation of self-focusing and defocusing in a SBN:60 crystal,” Master of Science thesis (Rose-Hulman Institute of Technology, Terre Haute, Ind., 1996).

1998 (1)

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

1995 (1)

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

1992 (1)

1990 (1)

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

1982 (1)

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. A 72, 46–51 (1982).

Bloch, G.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

Bosshard, C.

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

Breitling, D.

D. Breitling, A. Siahmakoun, “Laser beam self-focusing and defocusing in a SBN:60,” Presented at the OSA Annual Meeting, Rochester, N.Y., 20–24 Oct. 1996 (Optical Society of America, Washington, D.C.).

D. Breitling, “An investigation of self-focusing and defocusing in a SBN:60 crystal,” Master of Science thesis (Rose-Hulman Institute of Technology, Terre Haute, Ind., 1996).

Daisy, R.

Feinberg, J.

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. A 72, 46–51 (1982).

Fischer, B.

Günter, P.

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, Berlin, 1988, 1989), Vols. 61 and 62.

Hagan, D. J.

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

Horowitz, M.

Huignard, J.-P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, Berlin, 1988, 1989), Vols. 61 and 62.

Lotscher, A.

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

Marquez Aguilar, P. A.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

Ryf, R.

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

Said, A. A.

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

Sanchez Mondragon, J. J.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

Sheik-Bahae, M.

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

Siahmakoun, A.

D. Breitling, A. Siahmakoun, “Laser beam self-focusing and defocusing in a SBN:60,” Presented at the OSA Annual Meeting, Rochester, N.Y., 20–24 Oct. 1996 (Optical Society of America, Washington, D.C.).

Stepanov, S.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

Van Stryland, E. W.

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

Wei, T.

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

Werner, O.

Zgonik, M.

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. A (1)

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. A 72, 46–51 (1982).

J. Opt. Soc. B (1)

R. Ryf, A. Lotscher, C. Bosshard, M. Zgonik, P. Günter, “Z-scan-based investigation of photorefractive self-defocusing in KNbO3 crystal,” J. Opt. Soc. B 15, 989–995 (1998).
[CrossRef]

Opt. Commun. (1)

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, “Z-scan experiments with cubic photorefractive crystal Bi12TiO20,” Opt. Commun. 118, 165–174 (1995).
[CrossRef]

Opt. Lett. (1)

Other (3)

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, Berlin, 1988, 1989), Vols. 61 and 62.

D. Breitling, A. Siahmakoun, “Laser beam self-focusing and defocusing in a SBN:60,” Presented at the OSA Annual Meeting, Rochester, N.Y., 20–24 Oct. 1996 (Optical Society of America, Washington, D.C.).

D. Breitling, “An investigation of self-focusing and defocusing in a SBN:60 crystal,” Master of Science thesis (Rose-Hulman Institute of Technology, Terre Haute, Ind., 1996).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a typical Z-scan experiment. Where P 1 and P 2 are detectors, d and D are distances of sample to aperture and beam waist to aperture, respectively.

Fig. 2
Fig. 2

Theoretical simulation of the normalized transmittance versus sample position.

Fig. 3
Fig. 3

Experimental apparatus for the Z-scan measurement. PR, polarization rotator; L 0, L 1, lenses; SH, shutter; det 1–3, detectors; SBN, SBN:60 sample.

Fig. 4
Fig. 4

Schematic shows the fractional laser power reflected and transmitted by BS1, SBN sample, and BS2 into detectors 1–3.

Fig. 5
Fig. 5

Plot of experimental Z-scan data: normalized transmittance versus the SBN position with an extraordinary Ar+ beam with (a) incident laser power, 16.3 mW; (b) incident laser power, 2.5 mW.

Fig. 6
Fig. 6

Plot of experimental Z-scan data: normalized transmittance versus the SBN position with (a) o-polarized Ar+ incident laser, (b) e-polarized He–Ne incident laser.

Equations (27)

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

Eiz, r, t=E0tw0wzexp-r2wz2×exp-ikz ikr22Rz+iξz,
Eez, r, t=Eiz, r, texp-αL2expiΔφ,
Δφx, y, z=-ΔnkL.
Δno=-12 no3r13Eysc=-22 KBTeπ no4r13w0ywz3exp-2x2+y2wz2,
Δneo=-12 ne3r33Eysc=-22 KBTeπ ne4r33w0ywz3exp-2x2+y2wz2,
Δφx, y, z=Δφ0zywzexp-2x2+y2wz2,
Δφ0z=22 KBTeπ neff4reffkL w0wz2,
expiΔφx, y, z=miΔφ0zmm!ywzm×exp-2mx2+y2wz2.
Eex, y, z=E0w0wzexp-ikz+iζz×miΔφ0zmm!ywzm×exp-2m+1x2+y2wz2-ik x2+y22Rz,
Eax, y, z=Ei0, 0, zexp-ikd+iζz×miΔφ0zmWm022m2m+1m/2m!Wm×exp-r2Wm2exp-ik r22Rm,
Wm0=wz22m+11/2,
Wm=Wm0g2+d/dm21/2,
dm=k2 Wm02,
Rm=d1-gg2+d/dm2-1,
g=1+d/Rz,
PTΔφz=12η02πdθ 0a |Ear, z|2rdr=πη0a |Ear, z|2rdr.
Tz=PTΔφz/SPi,
S=1-exp-2a2/wa2,
wa=w01+D2/z021/2.
P0=P1+P2+P3,
T1=P1+P2P1+P2+P3,
T2=P1P1+P2.
S=12P1fP2f,
PT¯=R1R2P2zP3zP0=1-T11-T2P2zP3zP0,
PC¯z=R1T2P1zP3zP0=1-T1T2P1zP3zP0,
TNz=1SP¯CzP¯Tz=TAzS=R2ST2P1zP2z=1S2P1zP2z.
TNpz=TNczTNgz,

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