Abstract

We show theoretically and experimentally that the photovoltaic nonlinearity that gives rise to spatial solitons can be switched from self-defocusing to self-focusing (or vice versa) by use of background illumination. This raises the possibility of bright photovoltaic solitons in LiNbO3.

© 1998 Optical Society of America

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  1. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
    [CrossRef] [PubMed]
  2. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef] [PubMed]
  3. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
    [CrossRef]
  4. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
    [CrossRef]
  5. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
    [CrossRef]
  6. M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
    [CrossRef] [PubMed]
  7. M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
    [CrossRef]
  8. S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
    [CrossRef]
  9. Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
    [CrossRef]
  10. The term “focused” is used to distinguish the narrow beam focused to the input face of the crystal from the uniform-background beam. It should not be confused with the terms “self-focused” and “self-defocused,” which describe the output beam at steady state.
  11. We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
    [CrossRef]

1997

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
[CrossRef]

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

1995

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

1994

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

1992

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

1982

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Baltz, R.

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Bashaw, M.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Bian, S.

S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
[CrossRef]

Chen, Z.

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

DiPorto, P.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Fejer, M.

Fejer, M. M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Festl, H.

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

Frejlich, J.

S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
[CrossRef]

Hertel, P.

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Kratzig, E.

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Maker, P.

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Muller, R.

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Ringhofer, K.

S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
[CrossRef]

Salamo, G.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Sánchez-Mondragón, J. J.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Segev, M.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

Shih, M.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Stepanov, S.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Taya, M.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

Valley, G. C.

M. Segev, G. C. Valley, M. Bashaw, M. Taya, and M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Vysloukh, V.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Wilson, D.

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Electron. Lett.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995); Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. Bian, J. Frejlich, and K. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997).
[CrossRef]

Z. Chen, M. Segev, D. Wilson, R. Muller, and P. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992); G. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994); D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995); M. Segev, M. Shih, and G. C. Valley, J.??Opt. Soc. Am. B 13, 706 (1996).
[CrossRef] [PubMed]

Phys. Status Solidi B

We measure interferometrically ?333=1.14?311, but cases in which ?311>?333 have been reported in, e.g., H. Festl, P. Hertel, E. Kratzig, and R. Baltz, Phys. Status Solidi B 113, 157 (1982); B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Non-Centrosymmetric Materials (Gordon & Breach, Philadelphia, Pa., 1992).
[CrossRef]

Other

The term “focused” is used to distinguish the narrow beam focused to the input face of the crystal from the uniform-background beam. It should not be confused with the terms “self-focused” and “self-defocused,” which describe the output beam at steady state.

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Figures (3)

Fig. 1
Fig. 1

(a) Beam profile. (b) Self-defocusing Δn for Ib=0. (c)  Self-focusing Δn when an orthogonally polarized background beam is added. Here Δn0<0 (as in LiNbO3).

Fig. 2
Fig. 2

Soliton existence curve for open-circuit bright photovoltaic solitons, showing the normalized FWHM as a function of u0. Inset, beam profile for u0=0.1. Crosses, experimental data points.

Fig. 3
Fig. 3

(a) 14µm FWHM input beam. (b)  Regularly diffracting 72µm output beam at t=0 (before E forms). (c)  Self-defocused output with Ib=0. (d)  Self-focused 35µm output beam with an orthogonally polarized background beam; I0=0.8 mW/cm2 and Ib=0.7 mW/cm2. (e)  Same as (d), except that I0=0.4 mW/cm2. (f)  Output beam when both beams are e polarized; I0=0.9 mW/cm2 and Ib=0.7 mW/cm2. The output beam in (f) shows little change from that in (b) (it self-focuses to 55 µm).

Equations (8)

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

sA2+Ib+IdNd-Ndi-γnNdi=0,
¯·J¯=¯·qμnE¯+KBTμ¯n+κijjsNd-Ndi×A2+κIbiˆ=0,
¯·E¯+q/εsn+NA-Ndi=0,
z-i2k2x2Ax, z=iknbΔnEAx, z,
EJ-κijjsNdI+κIbqμsNdNAγI+Ib+Id.
E=-NAγκijjI+κIbqμI+Ib+Id.
E=-NAγκijjqμ1+δIb-IdI+Ib+Id.
Δn=Δn0+Δn0Ibδ/Ix+Ib,

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