Abstract

We present a theoretical analysis of the stability of photorefractive spatial solitons along with experimental results that show that the solitons are stable for small-scale perturbations but break down when the perturbations exhibit a transverse scale comparable with the soliton size (cross section).

© 1994 Optical Society of America

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References

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  1. M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
    [CrossRef] [PubMed]
  2. B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
    [CrossRef]
  3. G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
    [CrossRef] [PubMed]
  4. M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
    [CrossRef]
  5. G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
    [CrossRef] [PubMed]
  6. Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
    [CrossRef]

1994

1993

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

1992

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

1990

Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
[CrossRef]

Crosignani, B.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

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

DiPorto, P.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Duree, G.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Engin, D.

Fischer, B.

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

Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
[CrossRef]

Neurgaonkar, R. R.

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Ophir, Y.

Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
[CrossRef]

Salamo, G.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Segev, M.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

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

Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
[CrossRef]

Sharp, E.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Shultz, J.

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

Shultz, J. L.

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Yariv, A.

G. Duree, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, Opt. Lett. 19, 1195 (1994).
[CrossRef] [PubMed]

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef]

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

J. Opt. Soc. Am. B

Opt. Commun.

Because beam fanning is a result of energy-exchange interactions (generated by diffusion fields) between the beam and scattered noise, we use two separate effects to eliminate it: (i) for a beam size that is much smaller than 100 μm, the cross section for interaction with noise in directions that differ significantly from z is very small [seeM. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990)]; (ii) we operate at external voltages that generate space-charge fields that are much larger than the diffusion field1,2: E0 ≫ Ed ≈(kBT/q)[(∂I/∂x)/I] ≈ (kBT/ql), which is ≈8 V/cm in our experiments.
[CrossRef]

Opt. Lett.

Opt. Photon. News

M. Segev, A. Yariv, G. Salamo, G. Duree, J. Shultz, B. Crosignani, P. DiPorto, E. Sharp, Opt. Photon. News 4(12), 9 (1993).
[CrossRef]

Phys. Rev. Lett.

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

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Horizontal and vertical cross sections of the propagating diffracted beam (zero field, left column) and soliton beam (right column) at various planes (inside the PR crystal) in the presence of small index perturbations. The waveforms are normalized to the maximal amplitudes in each plane. The horizontal and vertical beam spot sizes (wH and wV) are calculated according to a Gaussian fit.

Fig. 2
Fig. 2

Horizontal and vertical cross sections of the propagating beam with zero (left column), 400-V/cm (middle column), and 1000-V/cm (right column) external fields at different planes (inside the PR crystal) in the presence of large index perturbations. The waveforms are normalized to the maximal amplitudes in each plane.

Equations (13)

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( z - i 2 k 2 x 2 ) A ( x , z ) = i k n 1 δ n ( x , z ) A ( x , z ) ,
δ n ( x , z ) = 1 A ( x , z ) 2 × A ( x - ρ , z ) A * ( x + ρ , z ) g ( ρ , ρ ) d ρ d ρ ,
g ( ρ , ρ ) = δ n ^ ( q 1 , q 2 ) exp [ i ( q 1 ρ + q 2 ρ ) ] d q 1 d q 2
A ( x , z ) = U ( x ) exp ( i γ z ) ,
γ - a U U + b ( U U ) 2 = 0 ,
U ( x ) = U 0 [ sech ( α x ) ] D ,
U ( x ) = U 0 exp ( - α 2 x 2 ) ,
z ( A A * ) + i 2 k ( A 2 A * x 2 - A * 2 A x 2 ) = 0 ,
A ( x , z ) = U ( 0 ) ( x ) exp ( i γ z ) + U ( 1 ) ( x , z ) ,
{ U ( 0 ) [ U z ( 1 ) * + i γ U ( 1 ) * ] + i 2 k [ U ( 0 ) U x x ( 1 ) * - U ( 1 ) * U x x ( 0 ) ] } × exp ( i γ z ) + { U ( 0 ) [ U z ( 1 ) - i γ U ( 1 ) ] + i 2 k [ U ( 1 ) U x x ( 0 ) - U ( 0 ) U x x ( 1 ) ] } exp ( - i γ z ) = 0 ,
U z ( 1 ) - i γ U ( 1 ) + ( i / 2 k ) { [ U ( 1 ) U x x ( 0 ) / U ( 0 ) ] - U x x ( 1 ) } = 0.
U z ( 1 ) - ( i / 2 k ) U x x ( 1 ) = 0.
d d z - U ( 1 ) d x = 0 ,

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