Abstract

Numerical simulations show that channel waveguides can be self-written in photosensitive materials. As the waveguide evolves, its shape remains approximately constant, even though its depth and width change. We find an exact solution that describes this evolution, which we show to be self-similar. A wide variety of single-peaked beams form waveguides that converge to this solution.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1998 (1)

T. M. Monro, L. Poladian, and C. M. de Sterke, Phys. Rev. E 57, 1104 (1998).
[CrossRef]

1996 (2)

1993 (1)

1992 (1)

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

1991 (2)

1982 (1)

S. V. Manakov, Zh. Eksp. Teor. Fiz. 83, 68 (1982).

Aitchison, J. S.

An, S.

Blumen, G. W.

G. W. Blumen and J. D. Cole, Similarity Methods for Differential Equations (Springer-Verlag, New York, 1974).
[CrossRef]

Cole, J. D.

G. W. Blumen and J. D. Cole, Similarity Methods for Differential Equations (Springer-Verlag, New York, 1974).
[CrossRef]

de Sterke, C. M.

T. M. Monro, L. Poladian, and C. M. de Sterke, Phys. Rev. E 57, 1104 (1998).
[CrossRef]

T. M. Monro, C. M. de Sterke, and L. Poladian, J. Opt. Soc. Am. B 13, 2824 (1996).
[CrossRef]

Frisken, S. J.

Jackel, J. L.

Kewitsch, A. S.

Leaird, D. E.

Levi, D.

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Manakov, S. V.

S. V. Manakov, Zh. Eksp. Teor. Fiz. 83, 68 (1982).

Menyuk, C. R.

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Monro, T. M.

T. M. Monro, L. Poladian, and C. M. de Sterke, Phys. Rev. E 57, 1104 (1998).
[CrossRef]

T. M. Monro, C. M. de Sterke, and L. Poladian, J. Opt. Soc. Am. B 13, 2824 (1996).
[CrossRef]

Oliver, M. K.

Poladian, L.

T. M. Monro, L. Poladian, and C. M. de Sterke, Phys. Rev. E 57, 1104 (1998).
[CrossRef]

T. M. Monro, C. M. de Sterke, and L. Poladian, J. Opt. Soc. Am. B 13, 2824 (1996).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap.??16.

Silberberg, Y.

Sipe, J. E.

Smith, P. W. E.

Weiner, A. M.

Winternitz, P.

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Yariv, A.

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Rev. E (1)

T. M. Monro, L. Poladian, and C. M. de Sterke, Phys. Rev. E 57, 1104 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

S. V. Manakov, Zh. Eksp. Teor. Fiz. 83, 68 (1982).

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap.??16.

G. W. Blumen and J. D. Cole, Similarity Methods for Differential Equations (Springer-Verlag, New York, 1974).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Similarity solutions of the self-writing problem p=1. M̃ is the mode shape and Ñ is the refractive-index shape.

Fig. 2
Fig. 2

Inverse width of the refractive index versus T at various values of Z (p=1; simulation results).

Fig. 3
Fig. 3

Width of the refractive index versus T on a log-linear plot at various values of Z (p=2; simulation results).

Fig. 4
Fig. 4

ZB1/2 versus T (p=1; simulation results), which gives a straight line, in agreement with the similarity prediction. The solid line is a straight-line fit to the data.

Fig. 5
Fig. 5

Shape of the refractive-index profile for a triangular input beam at different Z (p=1; simulation results).

Equations (11)

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

iEZ+122EY2+NE=0,
NT=EE*p.
EY, Z, T=MY, TexpiβTZ,
P=-MY, T2dY.
Ỹ=YϕT
MY, T=ϕT1/2M̃Ỹ,
NY, T=ϕT2ÑỸ,
βT=ϕT2,
ϕT=PP̃pϕTp-1
12M̃Ỹ+ÑỸ-1M̃Ỹ=0,
2ÑỸ+ỸÑỸ=M̃Ỹ2p.

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