Abstract

The process of thermal annealing of K+–Na+ ion-exchanged waveguides in soda lime glass is characterized and compared with a simple theoretical model. The discrepancies between theory and experiments in the case of initially thick guides disappear if the existence of a stress-induced contribution to the refractive index is assumed that is not proportional to the concentration of the doping ions. The results obtained for initially thin guides are exploited for the design of annealed single-mode channel waveguides: 0.4-dB coupling losses with commercial single-mode fibers at λ = 1.321 μm were measured.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).
  6. J. M. White, P. F. Heidrich, Appl. Opt. 15, 151 (1976).
    [CrossRef] [PubMed]
  7. C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
    [CrossRef]
  8. C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
    [CrossRef]
  9. V. I. Smirnov, Corso di Matematica Superiore (Editori Riuniti, Rome, 1985), Vol. IV.
  10. G. M. Bartenev, N. N. Scheglova, J. Non-Cryst. Solids 37, 285 (1980).
    [CrossRef]

1989 (1)

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

1988 (4)

S. I. Najafi, Appl. Opt. 27, 3728 (1988).
[CrossRef] [PubMed]

J. Albert, G. L. Yip, Appl. Opt. 27, 4837 (1988).
[CrossRef] [PubMed]

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

1985 (1)

1981 (1)

E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).

1980 (1)

G. M. Bartenev, N. N. Scheglova, J. Non-Cryst. Solids 37, 285 (1980).
[CrossRef]

1976 (1)

Aksenov, E. T.

E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).

Albert, J.

Bartenev, G. M.

G. M. Bartenev, N. N. Scheglova, J. Non-Cryst. Solids 37, 285 (1980).
[CrossRef]

Carnera, A.

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

Cheng, H. C.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

De Bernardi, C.

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

De Franceschi, R.

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

Heidrich, P. F.

Lipovskii, A. A.

E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).

Malvicino, C.

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

Miliou, A.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

Morasca, S.

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

Moro, L.

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

Morra, M.

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

Najafi, S. I.

Pavlenko, A. V.

E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).

Ramaswamy, R. V.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

Scheglova, N. N.

G. M. Bartenev, N. N. Scheglova, J. Non-Cryst. Solids 37, 285 (1980).
[CrossRef]

Smirnov, V. I.

V. I. Smirnov, Corso di Matematica Superiore (Editori Riuniti, Rome, 1985), Vol. IV.

Srivastava, R.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

White, J. M.

Yip, G. L.

Zhenguang, H.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, IEEE J. Quantum Electron. 25, 1889 (1989).
[CrossRef]

J. Appl. Phys. (1)

C. De Bernardi, C. Malvicino, S. Morasca, M. Morra, J. Appl. Phys. 63, 234 (1988).
[CrossRef]

J. Mod. Opt. (1)

C. De Bernardi, R. De Franceschi, C. Malvicino, S. Morasca, L. Moro, M. Morra, A. Carnera, J. Mod. Opt. 35, 907 (1988).
[CrossRef]

J. Non-Cryst. Solids (1)

G. M. Bartenev, N. N. Scheglova, J. Non-Cryst. Solids 37, 285 (1980).
[CrossRef]

Opt. Lett. (1)

Soviet Phys. Tech. Phys. (1)

E. T. Aksenov, A. A. Lipovskii, A. V. Pavlenko, Soviet Phys. Tech. Phys. 26, 136 (1981).

Other (1)

V. I. Smirnov, Corso di Matematica Superiore (Editori Riuniti, Rome, 1985), Vol. IV.

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Figures (4)

Fig. 1
Fig. 1

Variation of the TE Δn0 versus τa/τ.

Fig. 2
Fig. 2

Annealing of the TE index profile of a thin guide.

Fig. 3
Fig. 3

Annealing of the TE index profile of a thick guide.

Fig. 4
Fig. 4

Best fit of the experimental points on the TE dispersion curves of the terfc profile for a thin and a thick guide with τa/τ = 1.

Equations (5)

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

Δ n ( x ) = Δ n 0 f ( x D τ ) = Δ n 0 f ( ξ ) ,
Δ N ( x ) = 1 π D a τ a Δ N 0 D τ × F ( ξ 0 ) exp [ - ( x - ξ 0 D τ D a τ a ) 2 ] Δ ξ ,
Δ n ( x ) = Δ n 0 π ( D τ D a τ a ) 1 / 2 × { 0 + f ( ξ ) exp [ - ( x - ξ D τ D a τ a ) 2 ] d ξ + 0 + f ( ξ ) exp [ - ( x + ξ D τ D a τ a ) 2 ] d ξ } .
Δ n 0 ( τ a / τ ) = Δ n 0 ( 1 + D a τ a D τ ) 1 / 2 ,
Δ n 0 ( τ a / τ ) = 2 π Δ n 0 arctan ( D τ D a τ a ) 1 / 2 .

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