Abstract

We study the possibility of self-trapping of an optical beam in a photorefractive medium under the combined influence of diffraction and self-scattering (two-wave mixing) of its spatial frequency components. We investigate the spectrum of solutions for the resulting photorefractive spatial solitons and discuss their unique properties. Design considerations and material requirements for experimental realization of these solitons, together with specific examples, are given.

© 1993 Optical Society of America

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  1. M. Hercher, J. Opt. Soc. Am. 54, 563 (1964).
  2. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [Crossref]
  3. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  4. J. E. Bjorkholm and A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
    [Crossref]
  5. A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
    [Crossref]
  6. J. S. Aitchinson, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. Smith, Opt. Lett. 15, 471 (1990).
    [Crossref]
  7. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [Crossref] [PubMed]
  8. D. A. Temple and C. Warde, J. Opt. Soc. Am. B 3, 337 (1986).
    [Crossref]
  9. S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 8.
  10. B. Crosignani and A. Yariv, J. Opt. Soc. Am. A 1, 1034 (1984).
    [Crossref] [PubMed]
  11. J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.
  12. J. Feinberg and R. W. Hellwarth, Opt. Lett. 5, 519 (1980); Opt. Lett. 6, 257 (1981).
    [Crossref]
  13. M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
    [Crossref]
  14. M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
    [Crossref]
  15. A. V. Mamaev and V. V. Shkunov, Sov. J. Quantum Electron. 19, 1199 (1990).
    [Crossref]
  16. F. Vachss and L. Hesselink, J. Opt. Soc. Am. A 5, 690 (1988).
    [Crossref]
  17. G. C. Valley, J. Opt. Soc. Am. B 9, 1440 (1992).
    [Crossref]
  18. M. Segev and A. Yariv, Opt. Lett. 16, 1938 (1991).
    [Crossref] [PubMed]
  19. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  20. A. Agranat, V. Leyva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
    [Crossref] [PubMed]
  21. R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
    [Crossref] [PubMed]
  22. B. Fischer and M. Segev, Appl. Phys. Lett. 54, 684 (1989).
    [Crossref]
  23. F. Ito and K. Kitayama, Appl. Phys. Lett. 59, 1932 (1991).
    [Crossref]

1992 (3)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

G. C. Valley, J. Opt. Soc. Am. B 9, 1440 (1992).
[Crossref]

1991 (2)

F. Ito and K. Kitayama, Appl. Phys. Lett. 59, 1932 (1991).
[Crossref]

M. Segev and A. Yariv, Opt. Lett. 16, 1938 (1991).
[Crossref] [PubMed]

1990 (4)

J. S. Aitchinson, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. Smith, Opt. Lett. 15, 471 (1990).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
[Crossref]

A. V. Mamaev and V. V. Shkunov, Sov. J. Quantum Electron. 19, 1199 (1990).
[Crossref]

1989 (2)

1988 (1)

1986 (1)

1985 (1)

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[Crossref]

1984 (1)

1980 (1)

1974 (1)

J. E. Bjorkholm and A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[Crossref]

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1964 (2)

M. Hercher, J. Opt. Soc. Am. 54, 563 (1964).

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Agranat, A.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

A. Agranat, V. Leyva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
[Crossref] [PubMed]

Aitchinson, J. S.

Ashkin, A.

J. E. Bjorkholm and A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[Crossref]

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[Crossref]

Bjorkholm, J. E.

J. E. Bjorkholm and A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Cronin-Golomb, M.

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

B. Crosignani and A. Yariv, J. Opt. Soc. Am. A 1, 1034 (1984).
[Crossref] [PubMed]

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 8.

Di Porto, P.

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 8.

Feinberg, J.

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
[Crossref]

B. Fischer and M. Segev, Appl. Phys. Lett. 54, 684 (1989).
[Crossref]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[Crossref]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Hellwarth, R. W.

Hercher, M.

M. Hercher, J. Opt. Soc. Am. 54, 563 (1964).

Hesselink, L.

Hofmeister, R.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Ito, F.

F. Ito and K. Kitayama, Appl. Phys. Lett. 59, 1932 (1991).
[Crossref]

Jackel, J. L.

Kitayama, K.

F. Ito and K. Kitayama, Appl. Phys. Lett. 59, 1932 (1991).
[Crossref]

Kwong, S. K.

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Leaird, D. E.

Leyva, V.

Mamaev, A. V.

A. V. Mamaev and V. V. Shkunov, Sov. J. Quantum Electron. 19, 1199 (1990).
[Crossref]

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Oliver, M. K.

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
[Crossref]

Segev, M.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

M. Segev and A. Yariv, Opt. Lett. 16, 1938 (1991).
[Crossref] [PubMed]

M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
[Crossref]

B. Fischer and M. Segev, Appl. Phys. Lett. 54, 684 (1989).
[Crossref]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Shkunov, V. V.

A. V. Mamaev and V. V. Shkunov, Sov. J. Quantum Electron. 19, 1199 (1990).
[Crossref]

Silberberg, Y.

Smith, P. W.

Solimeno, S.

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 8.

Temple, D. A.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Vachss, F.

Valley, G. C.

Vogel, E. M.

Warde, C.

Weiner, A. M.

White, J. O.

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Yagi, S.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Yariv, A.

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

M. Segev and A. Yariv, Opt. Lett. 16, 1938 (1991).
[Crossref] [PubMed]

A. Agranat, V. Leyva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
[Crossref] [PubMed]

B. Crosignani and A. Yariv, J. Opt. Soc. Am. A 1, 1034 (1984).
[Crossref] [PubMed]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Appl. Phys. Lett. (3)

M. Segev, Y. Ophir, and B. Fischer, Appl. Phys. Lett. 56, 1086 (1990).
[Crossref]

B. Fischer and M. Segev, Appl. Phys. Lett. 54, 684 (1989).
[Crossref]

F. Ito and K. Kitayama, Appl. Phys. Lett. 59, 1932 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

M. Hercher, J. Opt. Soc. Am. 54, 563 (1964).

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, Opt. Commun. 77, 265 (1990).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (4)

J. E. Bjorkholm and A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[Crossref] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

R. Hofmeister, A. Yariv, S. Yagi, and A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

A. V. Mamaev and V. V. Shkunov, Sov. J. Quantum Electron. 19, 1199 (1990).
[Crossref]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (3)

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 8.

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, in Photorefractive Materials and their Applications II, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

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Figures (2)

Fig. 1
Fig. 1

Schematic experimental geometry for the observation of a PR spatial soliton in SBN.

Fig. 2
Fig. 2

Plot of the cross section of the light field amplitude U(x) of the PR soliton given as an example in the text. The vertical axis gives the amplitude in arbitrary units, and the horizontal axis x is in micrometers.

Equations (47)

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E ( r , z , t ) = 1 2 { exp [ i ( k z - ω t ) ] × E ( q , r ) exp [ i ( β q - k ) z ] f ( q , z ) d q + c . c . ] 1 2 [ A ( r , z ) exp [ i ( k z - ω t ) ] + c . c . } ,
E ( q , r ) = 1 2 π ( μ 0 0 n 1 ) 1 / 2 exp ( i q · r ) .
( z - i 2 k r 2 ) A ( r , z ) = i k n 1 δ n ( r , z ) A ( r , z ) .
δ n ( r , z ) = ( 1 / I 0 ) { a 1 ( z ) exp [ i ( q 1 · r + β q 1 z ) ] a 2 * ( z ) × exp [ - i ( q 2 · r + β q 2 z ) ] δ n ^ ( q 1 , q 2 ) + c . c . } ,
δ n ^ ( q 1 , q 2 ) = - ω 2 c n 1 3 r eff ( q 1 , q 2 ) E m ( q 1 , q 2 ) ( e 1 · e 2 * ) ,
E m ( q 1 , q 2 ) = E p ( q 1 , q 2 ) E d ( q 1 , q 2 ) - i E 0 E 0 + i [ E d ( q 1 , q 2 ) + E p ( q 1 , q 2 ) ] ,
E 1 = E 0 ( E 0 / E p ) 2 + [ ( E p / E d ) + 1 ] 2 , E 2 = E p ( E 0 2 + E d 2 + E d E p ) E 0 2 + ( E d + E p ) 2 .
δ n ( r , z ) = 1 A ( r , z ) 2 d q 1 d q 2 f ( q 1 , z ) f * ( q 2 , z ) E ( q 1 , r ) × E * ( q 2 , r ) exp [ i ( β q 1 - β q 2 ) z ] δ n ^ ( q 1 , q 2 ) .
A ( r , z ) = U ( r ) exp ( i γ z ) ,
U ( r ) = ± U ( - r ) .
δ n ^ ( q 1 , q 2 ) = g ( ρ , ρ ) exp [ - i ( q 1 · ρ + q 2 · ρ ) d ρ d ρ ,
δ n ( r , z ) = 1 A ( r , z ) 2 × A ( r - ρ , z ) A * ( r + ρ , z ) g ( ρ , ρ ) d ρ d ρ .
( z - i 2 k r 2 ) A ( r , z ) = i k n 1 1 A * ( r , z ) A ( r - ρ , z ) A * ( r + ρ , z ) g ( ρ , ρ ) d ρ d ρ .
( γ - 1 2 k r 2 ) U ( r ) = k n 1 1 U * ( r ) U ( r - ρ ) U * ( r + ρ ) g ( ρ , ρ ) d ρ d ρ .
U ( r - ρ ) = U ( r ) - r U ( r ) · ρ + ½ [ r r U ( r ) ] : ρ ρ + ,
( z - i 2 k 2 x 2 ) A ( x , z ) = - i k n 1 I 11 1 A * | A x | 2 + i k 2 n 1 I 20 2 A x 2 + i k 2 n 1 I 02 A A * 2 A * x 2 + i k 4 n 1 I 22 1 A * | 2 A x | 2 ,
I m n = d ρ d ρ g ( ρ , ρ ) ρ m ρ n = exp [ i ( m + n ) π / 2 ] m q 1 m n q 2 n δ n ^ ( q 1 , q 2 ) q 1 = q 2 = 0 .
δ n ^ ( q 1 , q 2 ) = n = 0 m = 0 a m n q 1 m q 2 n ,
I m n = m ! n ! a m n exp [ i ( m + n ) π / 2 ] .
γ 1 U = - k 2 n 1 I 20 ( im ) d 2 U d x 2 ,
γ 2 U - 1 2 k d 2 U d x 2 = - k n 1 I 11 ( d U / d x ) 2 U + k 2 n 1 ( I 20 ( re ) + I 02 ( re ) ) d 2 U d x 2 + k 4 n 1 I 22 ( 1 U d 2 U d x 2 ) 2 .
γ 2 U - 1 2 k d 2 U d x 2 = - k n 1 I 11 ( d U / d x ) 2 U + k n 1 I 20 ( re ) d 2 U d x 2 + k 4 n 1 I 22 ( 1 U d 2 U d x 2 ) 2 .
γ U - 1 2 k U = - k n 1 I 11 U 2 U + k n 1 I 20 ( re ) U + k 4 n 1 I 22 U 2 U ,
γ - a U U + b ( U U ) 2 = 0 ,
a = 1 2 k + k n 1 I 20 ( re ) ,
b = k n 1 I 11 .
y = U U ,
a y + ( a - b ) y 2 - γ = 0
d y A - y 2 = d x D ,
y = A tanh ( α x ) ,
α = - A / D ,
U ( x ) = U 0 [ sech ( α x ) ] D .
D = a b - a = η 2 - η > 0 ,
U ( x ) = U 0 sech ( α x ) .
γ = a 2 a - b α 2 ,
γ + b ( U U ) 2 - α U U + c ( U U ) 2 = 0 ,
γ = γ ( 1 - c D 2 α 2 a - b ) ,
U ( x ) = U 0 exp ( - α 2 x 2 )
γ = - 2 b α 2 .
1 2 k + k n 1 I 20 ( re ) < k n 1 I 11 .
V = k r ( 2 n 1 Δ n ) 1 / 2 2
1 2 n 1 2 k + k n 1 I 20 ( re ) < k n 1 I 11 ,
E m ( q 1 , q 2 ) - E 1 ( q 1 , q 2 ) - E 0 ( E 0 / E p ) 2 + 1 .
δ n ^ ( q 1 , q 2 ) n 1 3 2 r 33 E 0 1 1 + ( E 0 0 r e P d ) 2 ( q 1 - q 2 ) 2 B 1 + d 2 ( q 1 - q 2 ) 2 .
r eff ( q 1 , q 2 ) = r 33 q 1 q 2 ( q 1 + q 2 ) 2 k 3 ,
- n 1 4 k 2 d 2 < B < - n 1 8 k 2 d 2 ,
( λ 2 e 2 P d 2 16 π 2 r 33 n 1 4 0 2 r 2 ) 1 / 3 < E 0 < ( λ 2 e 2 P d 2 8 π 2 r 33 n 1 4 0 2 r 2 ) 1 / 3 .

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