Abstract

Self-focusing and self-defocusing of light in two-wave mixing are investigated experimentally. Amplification and self-focusing are measured as functions of the frequency shift between signal and pump beams. A frequency dependence is found in Kramers–Kronig form, as is plausible by the analogy of photorefractive amplification and laser amplification. Reversal of the external dc field on the material or a change in the frequency shift between the signal and pump beams is found to change self-focusing to self-defocusing.

© 1997 Optical Society of America

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  1. M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
    [CrossRef] [PubMed]
  2. M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
    [CrossRef]
  3. K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
    [CrossRef] [PubMed]
  4. M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef] [PubMed]
  5. P. Yeh, Introduction to Photorefractive Non-Linear Optics (Wiley, New York, 1993).
  6. S. Weiss and B. Fischer, Opt. Quantum Electron. 22, S17 (1990).
    [CrossRef]
  7. M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
    [CrossRef] [PubMed]
  8. J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
    [CrossRef] [PubMed]

1996 (2)

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[CrossRef] [PubMed]

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

1995 (1)

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

1994 (1)

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

1993 (1)

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

1990 (2)

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

S. Weiss and B. Fischer, Opt. Quantum Electron. 22, S17 (1990).
[CrossRef]

Crosignani, B.

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

DiPorto, P.

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Fischer, B.

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

S. Weiss and B. Fischer, Opt. Quantum Electron. 22, S17 (1990).
[CrossRef]

Iturbe Castillo, M. D.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Malos, J.

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

Marquez Aguilar, P. A.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

Sánchez-Mondragón, J. J.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Segev, M.

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

Slekys, G.

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

Staliunas, K.

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[CrossRef] [PubMed]

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

Stepanov, S. I.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Tarroja, M. F. H.

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

Valley, C.

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Vaupel, M.

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[CrossRef] [PubMed]

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

Vysloukh, V.

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Weiss, C. O.

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[CrossRef] [PubMed]

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

Weiss, S.

S. Weiss and B. Fischer, Opt. Quantum Electron. 22, S17 (1990).
[CrossRef]

Yariv, A.

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Yeh, P.

P. Yeh, Introduction to Photorefractive Non-Linear Optics (Wiley, New York, 1993).

Appl. Phys. Lett. (2)

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990); M. Segev, B. Crosignani, and A. Yariv, Phys. Rev. Lett. 68, 923 (1992); G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgoankar, Phys. Rev. Lett. 71, 533 (1993); G. C. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995); M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996); M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. Valley, Opt. Lett. 21, 324 (1996).
[CrossRef] [PubMed]

M. D. Iturbe Castillo, P. A. Marquez Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1993); M. D. Iturbe Castillo, J. J. Sánchez-Mondragón, S. I. Stepanov, M. B. Klein, and B. A. Wechsler, Opt. Commun. 118, 515 (1994).
[CrossRef]

Opt. Quantum Electron. (1)

S. Weiss and B. Fischer, Opt. Quantum Electron. 22, S17 (1990).
[CrossRef]

Phys. Rev. A (3)

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[CrossRef] [PubMed]

J. Malos, M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 53, 3559 (1996).
[CrossRef] [PubMed]

K. Staliunas, M. F. H. Tarroja, G. Slekys, and C. O. Weiss, Phys. Rev. A 51, 4140 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. Segev, C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); M. Segev, M. Sinh, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Other (1)

P. Yeh, Introduction to Photorefractive Non-Linear Optics (Wiley, New York, 1993).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: RP, retardation plate; P1, P2, polarizers; M, mirror mounted upon a piezo stack; GP, glass plate; L1, lens; W, signal beam waist; IP, image plane; PM, photomultiplier.

Fig. 2
Fig. 2

Signal profiles recorded at a distance of one-half Rayleigh length behind the crystal with the crystal orientation such that the signal beam is diffracted into the pump beam: a, SSSF and two wave-mixing self-focusing at 1.0-Hz frequency shift; b, SSSF only; c, SSSF and two wave-mixing self-defocusing at 3.5-Hz frequency shift.

Fig. 3
Fig. 3

Nonlinear susceptibility χ3 and two-wave-mixing gain exponent Γ, as defined in Ref.  5, obtained from multiple recordings of the Gaussian signal beam (trace 1), with contributions of two-wave-mixing and SSSF, as function of the frequency shift Ω. Signal /pump intensity ratio, 3/2; pump intensity, 6 mW/cm2. Points, mean of four measurements. Error bars (standard deviation), fit with a dispersion function (dashed curve) and fit with a Lorentzian function (solid curve). Note the difference between the frequency of zero nonlinear susceptibility and the frequency of the gain line maximum, caused by SSSF.

Fig. 4
Fig. 4

Nonlinear susceptibility χ3 and two-wave-mixing gain exponent Γ, as defined in Ref.  5, obtained from multiple recordings of the Gaussian signal beam (trace 1), as function of the frequency shift Ω. Signal /pump intensity ratio, 1/14; pump intensity, 6 mW/cm2; E0=10 kV/cm. Points, mean of four measurements. Error bars (standard deviation), fit with a dispersion function (dashed curve) and fit with a Lorentzian function (solid curve). The frequencies of zero nonlinear susceptibility and the gain line maximum are identical because SSSF is absent.

Equations (1)

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χ3=n0w02/Lz1-w/w0Ep2/Es2

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