Abstract

Using the weighted residual method, formulas for calculating the propagation constant and field distributions of diffused channel waveguides are derived. The results obtained are more accurate than those of Marcatili’s method and agree well with those of the finite-element method.

© 1988 Optical Society of America

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References

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  1. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  2. R. M. Knox, P. P. Toulios, in Proceedings of the MRI Symposium on Millimeter Waves, J. Fox, ed. (Polytechnic Institute of Brooklyn, New York, 1970), p. 497.
  3. J. M. Hammer, Appl. Opt. 15, 319 (1976).
    [CrossRef] [PubMed]
  4. G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
    [CrossRef] [PubMed]
  5. C. Yeh, K. Ha, S. B. Dong, W. P. Brown, Appl. Opt. 18, 1490 (1979).
    [CrossRef] [PubMed]
  6. C. Pichot, Opt. Commun. 43, 169 (1982).
    [CrossRef]
  7. L. Qiao, S. She, Acta Opt. Sinica 6, 930 (1986).
  8. S. She, Acta Opt. Sinica 7, 544 (1987).
  9. S. She, L. Qiao, in Proceedings of the Sino-Japanese Joint Meeting on Optical Fiber Science and Electromagnetic Theory (China International Conference Center for Science and Technology, Beijing, 1987), p. 453.

1987

S. She, Acta Opt. Sinica 7, 544 (1987).

1986

L. Qiao, S. She, Acta Opt. Sinica 6, 930 (1986).

1982

C. Pichot, Opt. Commun. 43, 169 (1982).
[CrossRef]

1979

1977

1976

1969

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Brown, W. P.

Burns, W. K.

Dong, S. B.

Ha, K.

Hammer, J. M.

Hocker, G. B.

Knox, R. M.

R. M. Knox, P. P. Toulios, in Proceedings of the MRI Symposium on Millimeter Waves, J. Fox, ed. (Polytechnic Institute of Brooklyn, New York, 1970), p. 497.

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Pichot, C.

C. Pichot, Opt. Commun. 43, 169 (1982).
[CrossRef]

Qiao, L.

L. Qiao, S. She, Acta Opt. Sinica 6, 930 (1986).

S. She, L. Qiao, in Proceedings of the Sino-Japanese Joint Meeting on Optical Fiber Science and Electromagnetic Theory (China International Conference Center for Science and Technology, Beijing, 1987), p. 453.

She, S.

S. She, Acta Opt. Sinica 7, 544 (1987).

L. Qiao, S. She, Acta Opt. Sinica 6, 930 (1986).

S. She, L. Qiao, in Proceedings of the Sino-Japanese Joint Meeting on Optical Fiber Science and Electromagnetic Theory (China International Conference Center for Science and Technology, Beijing, 1987), p. 453.

Toulios, P. P.

R. M. Knox, P. P. Toulios, in Proceedings of the MRI Symposium on Millimeter Waves, J. Fox, ed. (Polytechnic Institute of Brooklyn, New York, 1970), p. 497.

Yeh, C.

Acta Opt. Sinica

L. Qiao, S. She, Acta Opt. Sinica 6, 930 (1986).

S. She, Acta Opt. Sinica 7, 544 (1987).

Appl. Opt.

Bell Syst. Tech. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Opt. Commun.

C. Pichot, Opt. Commun. 43, 169 (1982).
[CrossRef]

Other

R. M. Knox, P. P. Toulios, in Proceedings of the MRI Symposium on Millimeter Waves, J. Fox, ed. (Polytechnic Institute of Brooklyn, New York, 1970), p. 497.

S. She, L. Qiao, in Proceedings of the Sino-Japanese Joint Meeting on Optical Fiber Science and Electromagnetic Theory (China International Conference Center for Science and Technology, Beijing, 1987), p. 453.

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Figures (2)

Fig. 1
Fig. 1

Cross section of a diffused channel waveguide.

Fig. 2
Fig. 2

Dispersion curves for diffused channel guides5: solid curve, weighted residual method; dashed curve, finite element method; dotted curve, Marcatili’s method.

Equations (14)

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n 2 ( x , y ) = { n 0 2 , y > b n 1 2 , y = b n 2 ( y ) , | y | < b , | x | < a n 2 2 , y < b or | y | < b , | x | > a ,
2 ψ x 2 + 2 ψ y 2 + [ n 2 ( x , y ) n 2 2 n 1 2 n 2 2 P 2 ] ψ = 0 .
d 2 X d x 2 + ( P 2 2 P 2 ) X = 0 ,
d 2 Y d y 2 + f ( y ) Y = 0 ,
f ( y ) = { ( P 2 2 + Δ 0 2 ) y > V 2 Δ 2 ( y ) P 2 2 | x | < V 1 , | y | < V 2 , P 2 2 y < V 2 Δ 2 ( y ) = n 2 ( y ) n 2 2 n 1 2 n 2 2 , Δ 0 2 = n 2 2 n 0 2 n 1 2 n 2 2 .
X ( x ) = A cos ( P 2 2 P 2 x ) , | x | < V 1 .
Y ( y ) = { [ f ( V 2 ) ] 1 / 4 cos [ y c V 2 f ( ξ ) d ξ π 4 ] exp [ P 2 2 + Δ 0 2 ( y V 2 ) ] , y > V 2 [ f ( y ) ] 1 / 4 cos [ y c y f ( ξ ) d ξ π 4 ] , y c < y < V 2 , 2 2 [ f ( y ) ] 1 / 4 exp [ y y c f ( ξ ) d ξ ] , y < y c
tan [ y c V 2 f ( ξ ) d ξ π 4 ] = P 2 2 + Δ 0 2 1 P 2 2 .
0 Y ( y ) ( 2 x 2 + 2 y 2 n 2 n 2 2 n 1 2 n 2 2 P 2 ) X ( x ) Y ( y ) d y = 0 ,
d 2 X d x 2 τ 2 X = 0 ,
τ 2 = P 2 P 2 2 + K 2 , K 2 = V 2 V 2 Δ 2 ( y ) Y 2 ( y ) d y / Y 2 ( y ) d y .
X ( x ) = C exp [ τ ( | x | V 1 ) ] , | x | > V 1 .
tan ( P 2 2 P 2 V 1 ) = P 2 P 2 2 + K 2 P 2 2 P 2 .
n ( y ) = n 2 + n 2 n 1 4 V 2 2 [ ( y V 2 ) 2 4 V 2 2 ] ,

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