Abstract

Mode indices measurements for both the TE and TM modes have been made on planar waveguides by K+-ion exchange in soda-lime glass substrates. These were directed toward establishing formulas for evaluating the effective guide depth and diffusion constant for both the TE and the TM modes, given the diffusion temperature and time. The corresponding surface-index change can also be determined.

© 1985 Optical Society of America

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References

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  1. T. G. Giallorenzi, E. J. West, R. Kirk, R. Ginther, R. A. Andrews, Appl. Opt. 12, 1240 (1973).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. G. L. Yip, J. Finak, Opt. Lett. 9, 423 (1984).
    [CrossRef] [PubMed]
  8. K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
    [CrossRef]
  9. P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  10. S. S. Kuo, Computer Application of Numerical Methods (Addison-Wesley, Reading, Mass., 1972), p. 254.
  11. M. J. Box, Comput. J. 9, 67 (1966).
  12. R. H. Doremus, “Ion exchange,” in Ion Exchange, J. A. Marinsky, ed. (Dekker, New York, 1969), Vol. 2, pp. 1–42.

1984

G. L. Yip, J. Finak, Opt. Lett. 9, 423 (1984).
[CrossRef] [PubMed]

K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
[CrossRef]

1982

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

T. Findakly, B. Chen, Appl. Phys. Lett. 40, 549 (1982).
[CrossRef]

1978

G. H. Chartier, P. Jaussaud, A. D. de Oliveira, Electron. Lett. 14, 132 (1978).
[CrossRef]

1977

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

1973

1970

1966

M. J. Box, Comput. J. 9, 67 (1966).

Aksenov, E. T.

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

Andrews, R. A.

Box, M. J.

M. J. Box, Comput. J. 9, 67 (1966).

Chartier, G. H.

G. H. Chartier, P. Jaussaud, A. D. de Oliveira, Electron. Lett. 14, 132 (1978).
[CrossRef]

Chen, B.

T. Findakly, B. Chen, Appl. Phys. Lett. 40, 549 (1982).
[CrossRef]

De LaRue, R. M.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

de Oliveira, A. D.

G. H. Chartier, P. Jaussaud, A. D. de Oliveira, Electron. Lett. 14, 132 (1978).
[CrossRef]

Doremus, R. H.

R. H. Doremus, “Ion exchange,” in Ion Exchange, J. A. Marinsky, ed. (Dekker, New York, 1969), Vol. 2, pp. 1–42.

Finak, J.

G. L. Yip, J. Finak, Opt. Lett. 9, 423 (1984).
[CrossRef] [PubMed]

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

Findakly, T.

T. Findakly, B. Chen, Appl. Phys. Lett. 40, 549 (1982).
[CrossRef]

Garmire, E. M.

K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
[CrossRef]

Giallorenzi, T. G.

Ginther, R.

Honda, K.

K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
[CrossRef]

Jaussaud, P.

G. H. Chartier, P. Jaussaud, A. D. de Oliveira, Electron. Lett. 14, 132 (1978).
[CrossRef]

Jerominek, H.

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

Kirk, R.

Kukherev, A. V.

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

Kuo, S. S.

S. S. Kuo, Computer Application of Numerical Methods (Addison-Wesley, Reading, Mass., 1972), p. 254.

Laybourn, P. J. R.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Lipovskii, A. A.

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

Miller, C. A.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Opilski, Z.

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

Pavlenko, A. V.

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

Stewart, G.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Tien, P. K.

Ulrich, R.

West, E. J.

Wilkinson, C. D. W.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Wilson, K. E.

K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
[CrossRef]

Wojiala, K.

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

Yip, G. L.

Appl. Opt.

Appl. Phys. Lett.

T. Findakly, B. Chen, Appl. Phys. Lett. 40, 549 (1982).
[CrossRef]

Comput. J.

M. J. Box, Comput. J. 9, 67 (1966).

Electron. Lett.

G. H. Chartier, P. Jaussaud, A. D. de Oliveira, Electron. Lett. 14, 132 (1978).
[CrossRef]

IEEE J. Lightwave Technol.

K. Honda, E. M. Garmire, K. E. Wilson, IEEE J. Lightwave Technol. LT-2, 714 (1984).
[CrossRef]

IEEE J. Quantum Electron.

G. Stewart, C. A. Miller, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. De LaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

J. Opt. Soc. Am.

Opt. Appl.

J. Finak, H. Jerominek, Z. Opilski, K. Wojiala, Opt. Appl. 12, 11 (1982).

Opt. Lett.

Sov. Phys. Tech. Phys.

E. T. Aksenov, A. V. Kukherev, A. A. Lipovskii, A. V. Pavlenko, Sov. Phys. Tech. Phys. 27, 1472 (1982).

Other

S. S. Kuo, Computer Application of Numerical Methods (Addison-Wesley, Reading, Mass., 1972), p. 254.

R. H. Doremus, “Ion exchange,” in Ion Exchange, J. A. Marinsky, ed. (Dekker, New York, 1969), Vol. 2, pp. 1–42.

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Figures (3)

Fig. 1
Fig. 1

Theoretical dispersion curves (Gaussian profile) of the guided modes compared with measured mode indices for samples prepared at 400°C (diffusion times in minutes). (a) TE modes. (b) TM modes.

Fig. 2
Fig. 2

Effective guide depth d versus the square root of the diffusion time (temperatures in degrees C). (a) TE modes, (b) TM modes.

Fig. 3
Fig. 3

The relation between loge De (diffusion constant) and the inverse diffusion temperature 1/T.

Tables (2)

Tables Icon

Table 1 Measured Surface Index Change Δns and Effective Diffusion Constants De at Different Temperaturesa

Tables Icon

Table 2 Comparisons of Measured TE-Mode Indices with Theoretical Ones for Sample Prepared with T = 385°C and t = 24 h

Equations (4)

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

d = D e t ,
D e = C 1 exp ( C 2 / T ) m 2 sec 1 .
d = ( 60 C 1 ) 1 / 2 × 10 6 t 1 / 2 exp ( C 2 / 2 T ) μ m ,
d = ( m + ¾ ) π k 0 x ̅ t 0 [ n 2 ( x ̅ ) n e 2 ] 1 / 2 d x ̅ , m = 0 , 1 , 2 ,

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