Abstract

It is shown that, as a result of diffusion space-charge field effects, self-bouncing beam behavior is possible in photorefractive waveguides. The process is explicitly demonstrated by means of an exact Gaussian solution in the case of parabolic planar waveguides. The trajectory of these beams as well as their associated characteristics is given in terms of relevant parameters. Asymmetric modal states are also obtained for parabolic and other waveguide structures.

© 1996 Optical Society of America

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    [CrossRef]
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1995

D. N. Christodoulides, M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

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

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
[CrossRef] [PubMed]

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

D. Kip, S. Aulkemeyer, P. Moretti, Opt. Lett. 20, 1256 (1995).
[CrossRef] [PubMed]

1994

O. V. Lyubomudrov, V. V. Shkunov, J. Opt. Soc. Am. B 11, 1403 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

D. N. Christodoulides, M. I. Carvalho, Opt. Lett. 19, 1714 (1994).
[CrossRef] [PubMed]

1993

1992

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

Aguilar, P. A.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Aulkemeyer, S.

Buchal, C.

Carvalho, M. I.

Castillo, M. D.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Chandler, P. J.

Christodoulides, D. N.

Cronin-Golomb, M.

Crosignani, B.

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

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

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

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

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

Di Porto, P.

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

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

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

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

Duree, G. C.

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

Eason, R. W.

Engin, D.

Fisher, B.

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

Fleuster, M.

Fluck, D.

Garcia Quirino, G. S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Gunter, P.

Jaaskelainen, T.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

James, S. W.

Jeffrey, P. M.

Kamshilin, A. A.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

Kip, D.

Lyubomudrov, O. V.

Mondragon, J. J.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Moretti, P.

Neurgaonkar, R.

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

Prokofiev, V. V.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

Raita, E.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

Salamo, G.

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

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

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

Sanchez-Mondragon, J. J.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Segev, M.

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

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

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

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

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

Sharp, E.

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

Shih, M. F.

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

Shkunov, V. V.

Shultz, J. L.

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

Stepanov, S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

Townsend, P. D.

Valley, G. C.

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

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

Yariv, A.

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

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

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

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

Youden, K. E.

Zha, M.

Zhang, L.

Appl. Phys. Lett.

M. D. Castillo, P. A. Aguilar, J. J. Mondragon, S. Stepanov, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

A. A. Kamshilin, E. Raita, V. V. Prokofiev, T. Jaaskelainen, Appl. Phys. Lett. 67, 3242 (1995).
[CrossRef]

Electron. Lett.

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

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. A 50, R4457 (1994).
[CrossRef] [PubMed]

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

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

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

Evolution of the normalized intensity and displacement ν of a Gaussian beam propagating in a parabolic PR waveguide when (a) t = 1 and (b) t = 1.5.

Equations (13)

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i ϕ ξ + 1 2 ϕ s s s 2 2 ϕ + γ ( | ϕ | 2 ) s | ϕ | 2 ϕ = 0 ,
ϕ = ϕ 0 exp [ 1 2 ( s 2 + 4 γ s ) ] exp [ i 2 ( 1 + 4 γ 2 ) ξ ] ,
ϕ = A ( ξ ) exp [ η 2 2 ω 2 ( ξ ) ] exp { i [ θ ( ξ ) + η μ ( ξ ) + η 2 F ( ξ ) ] } ,
η = s ν ( ξ )
ω 2 = t 2 t 4 1 cos ( 2 ξ ) ,
A 2 = A 0 2 ( ω 0 / ω ) ,
F = 1 4 ω 2 d d ξ ( ω 2 ) ,
ν = ν 0 cos ( ξ ) + μ 0 sin ( ξ ) + 2 γ [ f ( ξ ) cos ( ξ ) g ( ξ ) sin ( ξ ) ] ,
μ = μ 0 cos ( ξ ) ν 0 sin ( ξ ) 2 γ [ f ( ξ ) sin ( ξ ) + g ( ξ ) cos ( ξ ) ] ,
θ = θ 0 + 1 2 0 ξ d ξ [ μ 2 ( ξ ) ν 2 ( ξ ) ω 2 ( ξ ) ] ,
f ( ξ ) = 1 2 α β ln { ( α + β α β ) [ α β cos ( ξ ) α + β cos ( ξ ) ] } ,
g ( ξ ) = 1 β ( α 2 β 2 ) 1 / 2 tan 1 [ β ( α 2 β 2 ) 1 / 2 sin ( ξ ) ] .
ϕ = ϕ 0 sech D ( s ) exp ( 2 γ s ) exp { i ( ξ / 2 ) [ D 2 ( 2 γ ) 2 ] } ,

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