Abstract

We propose a simple single-beam configuration for characterization of the amplitude, speed of growth, and polarization properties of the photoinduced refractive-index change that is due to a drift photorefractive mechanism of nonlinearity in crystals, namely, the modulation Z-scan technique, based on the modulation of an externally applied electric field. The results of a simple theoretical model developed for one-dimensional parabolic photorefractive lens formation in this configuration are illustrated by original experiments with a semi-insulating GaAs crystal at λ = 1.06 μm.

© 1996 Optical Society of America

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  1. P. Guenter, J.-P. Huignard, eds. , Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
    [CrossRef]
  2. S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
    [CrossRef]
  3. M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
    [CrossRef]
  4. G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
    [CrossRef] [PubMed]
  5. M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
    [CrossRef] [PubMed]
  6. Q. W. Song, Ch.-P. Zhang, P. J. Talbot, Appl. Opt. 32, 7266 (1993).
    [CrossRef] [PubMed]
  7. P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
    [CrossRef]
  8. H. L. Fang, R. L. Swafford, in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), p. 175.
  9. M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  10. P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.
  11. C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).
  12. A. Zozulya, D. Anderson, Phys. Rev. A 51, 1520 (1995); N. Korneev, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, M. Klein, B. Wechsler, J. Mod. Opt. 43, 311 (1996).
    [CrossRef] [PubMed]

1995

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

A. Zozulya, D. Anderson, Phys. Rev. A 51, 1520 (1995); N. Korneev, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, M. Klein, B. Wechsler, J. Mod. Opt. 43, 311 (1996).
[CrossRef] [PubMed]

1994

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

1993

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Q. W. Song, Ch.-P. Zhang, P. J. Talbot, Appl. Opt. 32, 7266 (1993).
[CrossRef] [PubMed]

1990

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Anderson, D.

A. Zozulya, D. Anderson, Phys. Rev. A 51, 1520 (1995); N. Korneev, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, M. Klein, B. Wechsler, J. Mod. Opt. 43, 311 (1996).
[CrossRef] [PubMed]

Bashaw, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Bloch, G.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

Crosignani, B.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Di Porto, P.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Fang, H. L.

H. L. Fang, R. L. Swafford, in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), p. 175.

Fejer, M. M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Gomez Sarabia, C. M.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

Hagan, D.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Iturbe Castillo, M. D.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

Marquez Aguilar, P. A.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

Neurgaonkar, R.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Salamo, G.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Sanchez Mondragon, J. J.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

Segev, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Song, Q. W.

Stepanov, S.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

Stepanov, S. I.

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Swafford, R. L.

H. L. Fang, R. L. Swafford, in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), p. 175.

Talbot, P. J.

Taya, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Valley, G. C.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Vysloukh, V.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Yariv, A.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Zhang, Ch.-P.

Zozulya, A.

A. Zozulya, D. Anderson, Phys. Rev. A 51, 1520 (1995); N. Korneev, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, M. Klein, B. Wechsler, J. Mod. Opt. 43, 311 (1996).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994); M. D. Iturbe Castillo, J. J. Sanchez Mondragon, S. Stepanov, M. B. Klein, B. A. Wechsler, Opt. Commun. 118, 515 (1995).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. Wei, D. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Opt. Commun.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, G. Bloch, Opt. Commun. 118, 165 (1995).
[CrossRef]

Phys. Rev. A

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

A. Zozulya, D. Anderson, Phys. Rev. A 51, 1520 (1995); N. Korneev, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, M. Klein, B. Wechsler, J. Mod. Opt. 43, 311 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. C. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993); M. Morin, G. Duree, G. Salamo, M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

Rep. Prog. Phys.

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Other

P. Guenter, J.-P. Huignard, eds. , Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
[CrossRef]

H. L. Fang, R. L. Swafford, in Ultrasensitive Laser Spectroscopy, D. S. Kliger, ed. (Academic, New York, 1983), p. 175.

P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, in Quantum Electronics and Laser Science Conference, Vol. 10 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1966), p. 212.

C. M. Gomez Sarabia, P. A. Marquez Aguilar, J. J. Sanchez Mondragon, S. Stepanov, V. Vysloukh, “Dynamics of photoinduced lens formation in photore-fractive Bi12TiO20 crystal under an external dc electric field,” J. Opt. Soc. Am. B (to be published).

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Figures (4)

Fig. 1
Fig. 1

Simplified configurations: A, for the standard Z-scan technique and B, for the modulation Z-scan technique in photorefractive crystals.

Fig. 2
Fig. 2

Experimental sample position (●) and input polarization angle (■) dependence of the output ac signal: GaAs, λ = 1.06 μm, Pinput ≅ 0.3 mW, and Ω/2π ≅ 3 kHz (the polarization angle is counted from the vertical direction corresponding to the [ 1 1 ¯ 0 ] crystallographic axis and the direction of application of the external field). Solid curves, fitted normalized theoretical dependencies: sin(2Θ) and that obtained from Eq. (3) for ΩτM0 ≅ 0.26 in the latter and in the former cases, respectively.

Fig. 3
Fig. 3

Experimental frequency dependence of the output ac signal obtained for three different input laser powers Pinput mW: (▲) 0.3, (●) 0.9, and (■) 1.8. GaAs, λ = 1.06 μm, z ≅ 5 cm. Solid curve, fitted theoretical curve corresponding to Eq. (3).

Fig. 4
Fig. 4

Theoretical curves showing the dependence of the absolute value of the modulation Z-scan output signal amplitude calculated from Eq. (3). F0/z0 = 1. ΩτM = a, 0.03; b, 0.1; c, 0.3; d, 1; e, 3; f, 10; g, 30.

Equations (5)

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

1 / F Ω ( z ) = 1 1 + ( z / z 0 ) 2 1 F 0 i Ω τ M ( 1 + i Ω τ M ) 2 .
T = F ( z ) { z 0 2 + [ F ( z ) z ] 2 } 1 / 2 1 + z F ( z ) .
T Ω z F 0 [ 1 + ( z / z 0 ) 2 ] [ i Ω τ M ( 1 + i Ω τ M ) 2 ] .
T Ω z F 0 [ 1 + ( z / z 0 ) 2 ] 2 1 i Ω τ M 0 ,
| T Ω , max ( z 0 ) | = z 0 / 4 F 0 = π ( E 0 d ) / 2 U λ / 2

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