Abstract

We study the optically induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and the relative power of the input beams and suggest an improved analytical model that describes the growth of single waveguides and the main features of their interaction in photosensitive materials.

© 2002 Optical Society of America

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References

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  1. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
    [CrossRef]
  3. S. Shoji and S. Kawata, Appl. Phys. Lett. 75, 737 (1999).
    [CrossRef]
  4. A. S. Kewitsch and A. Yariv, Opt. Lett. 21, 24 (1996).
    [CrossRef] [PubMed]
  5. A. S. Kewitsch and A. Yariv, Appl. Phys. Lett. 68, 455 (1996).
    [CrossRef]
  6. S. Marou and K. Ikuta, Appl. Phys. Lett. 76, 2656 (2000).
    [CrossRef]
  7. See, e.g., D. Engin, A. S. Kewitsch, and A. Yariv, J. Opt. Soc. Am. B 16, 1213 (1999), and references therein.
    [CrossRef]

2001 (1)

T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
[CrossRef]

2000 (1)

S. Marou and K. Ikuta, Appl. Phys. Lett. 76, 2656 (2000).
[CrossRef]

1999 (3)

See, e.g., D. Engin, A. S. Kewitsch, and A. Yariv, J. Opt. Soc. Am. B 16, 1213 (1999), and references therein.
[CrossRef]

S. Shoji and S. Kawata, Appl. Phys. Lett. 75, 737 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1996 (2)

A. S. Kewitsch and A. Yariv, Appl. Phys. Lett. 68, 455 (1996).
[CrossRef]

A. S. Kewitsch and A. Yariv, Opt. Lett. 21, 24 (1996).
[CrossRef] [PubMed]

De Sterke, C. M.

T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
[CrossRef]

Engin, D.

Ikuta, K.

S. Marou and K. Ikuta, Appl. Phys. Lett. 76, 2656 (2000).
[CrossRef]

Kawata, S.

S. Shoji and S. Kawata, Appl. Phys. Lett. 75, 737 (1999).
[CrossRef]

Kewitsch, A. S.

Marou, S.

S. Marou and K. Ikuta, Appl. Phys. Lett. 76, 2656 (2000).
[CrossRef]

Monro, T. M.

T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
[CrossRef]

Poladian, L.

T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
[CrossRef]

Segev, M.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Shoji, S.

S. Shoji and S. Kawata, Appl. Phys. Lett. 75, 737 (1999).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Yariv, A.

Appl. Phys. Lett. (3)

S. Shoji and S. Kawata, Appl. Phys. Lett. 75, 737 (1999).
[CrossRef]

A. S. Kewitsch and A. Yariv, Appl. Phys. Lett. 68, 455 (1996).
[CrossRef]

S. Marou and K. Ikuta, Appl. Phys. Lett. 76, 2656 (2000).
[CrossRef]

J. Mod. Opt. (1)

T. M. Monro, C. M. De Sterke, and L. Poladian, J. Mod. Opt. 48, 191 (2001).
[CrossRef]

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

Opt. Lett. (1)

Science (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Experimental data showing the collisions between two self-written waveguides. The power of the lower beam is 0.1 mW; the power of the upper beam is (a), (d) 0.1 mW, (b) 0.07 mW, and (c) 0.13 mW. The time delay between the lower and upper beams is (a)–(c) 0 s and (d) 2 s.

Fig. 2
Fig. 2

Numerically calculated changes in the refractive-index profile for different values of the intensity threshold, Ith: (a) 0, (b) 0.01, and (c) 0.025. For all the plots, the input power is P0.1, exposure time τ=1200, the beam width FWHM is 1.5, and the model parameters are A=0.0025, n0=1.53, Δns=0.02, t0=1 ms, and a=1 µm.

Fig. 3
Fig. 3

Numerically calculated changes in the refractive-index profile for colliding waveguides formed by inclined input beams. In (a)–(d) the collision angle is 1°, the power of the upper input beam is P=0.1, and the lower-beam power P is (a) 0.1, (b) 0.092, (c) 0.077, (d) 0.063. In (e)–(h) the power of both beams is P=0.1, and the collision angle is (e) 1°, (f) 2°, (g) 2.5°, (h) 3°. For all plots Ith=0.025, and the other parameters are the same as in Fig. 2.

Equations (4)

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

iEr,z,τz+D2E+νr,z,τE=0,
Δnτ=A1-ΔnΔnsE2-Ith,E2Ith0,E2<Ith,
Δnx=Δns,x<d/20,xd/2,
Ex,z=Ith expiβz×cosqx/cosqd/2,x<d/2exp-px-d/2,xd/2,

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