Abstract

Propagation constants of weakly guiding optical fibers with arbitrary shapes can be efficiently calculated through a limited circular Fourier expansion of the wave equation, with a direct numerical integration.

© 1989 Optical Society of America

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References

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  1. C. Yeh, K. Ha, S. B. Dong, W. P. Brown, Appl. Opt. 18, 1490 (1979).
    [Crossref] [PubMed]
  2. A. W. Snyder, X. H. Zheng, J. Opt. Soc. Am. A 3, 600 (1986).
    [Crossref]
  3. E. A. J. Marcatili, A. A. Hardy, IEEE J. Quantum Electron. 24, 766 (1988).
    [Crossref]
  4. C. H. Henry, B. H. Verbeek, IEEE J. Lightwave Technol. 7, 308 (1989).
    [Crossref]
  5. R. M. Knox, P. P. Toulios, in Proceedings of MRI Symposium on Submillimeter Waves, J. Fox, ed. (Polytechnic, New York, 1970), pp. 497–516.
  6. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  7. A. Kumar, D. F. Clark, B. Culshaw, Opt. Lett. 13, 1129 (1988).
    [Crossref] [PubMed]

1989 (1)

C. H. Henry, B. H. Verbeek, IEEE J. Lightwave Technol. 7, 308 (1989).
[Crossref]

1988 (2)

E. A. J. Marcatili, A. A. Hardy, IEEE J. Quantum Electron. 24, 766 (1988).
[Crossref]

A. Kumar, D. F. Clark, B. Culshaw, Opt. Lett. 13, 1129 (1988).
[Crossref] [PubMed]

1986 (1)

1979 (1)

1969 (1)

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

Brown, W. P.

Clark, D. F.

Culshaw, B.

Dong, S. B.

Ha, K.

Hardy, A. A.

E. A. J. Marcatili, A. A. Hardy, IEEE J. Quantum Electron. 24, 766 (1988).
[Crossref]

Henry, C. H.

C. H. Henry, B. H. Verbeek, IEEE J. Lightwave Technol. 7, 308 (1989).
[Crossref]

Knox, R. M.

R. M. Knox, P. P. Toulios, in Proceedings of MRI Symposium on Submillimeter Waves, J. Fox, ed. (Polytechnic, New York, 1970), pp. 497–516.

Kumar, A.

Marcatili, E. A. J.

E. A. J. Marcatili, A. A. Hardy, IEEE J. Quantum Electron. 24, 766 (1988).
[Crossref]

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

Snyder, A. W.

Toulios, P. P.

R. M. Knox, P. P. Toulios, in Proceedings of MRI Symposium on Submillimeter Waves, J. Fox, ed. (Polytechnic, New York, 1970), pp. 497–516.

Verbeek, B. H.

C. H. Henry, B. H. Verbeek, IEEE J. Lightwave Technol. 7, 308 (1989).
[Crossref]

Yeh, C.

Zheng, X. H.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

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

IEEE J. Lightwave Technol. (1)

C. H. Henry, B. H. Verbeek, IEEE J. Lightwave Technol. 7, 308 (1989).
[Crossref]

IEEE J. Quantum Electron. (1)

E. A. J. Marcatili, A. A. Hardy, IEEE J. Quantum Electron. 24, 766 (1988).
[Crossref]

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

Opt. Lett. (1)

Other (1)

R. M. Knox, P. P. Toulios, in Proceedings of MRI Symposium on Submillimeter Waves, J. Fox, ed. (Polytechnic, New York, 1970), pp. 497–516.

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Figures (2)

Fig. 1
Fig. 1

Normalized propagation constant B = [(β/k)2clad]/[(coreclad) versus the normalized frequency for the dominant mode of a triangular fiber (an equilateral triangle). The solid curve is calculated from Ref. 1; the points are calculated by our method.

Fig. 2
Fig. 2

Same as in Fig. 1 for an elliptical fiber.

Tables (2)

Tables Icon

Table 1 Normalized Propagation Constants for the Dominant Mode of a Rectangular Fiber for Various Calculationsa

Tables Icon

Table 2 Normalized Propagation Constants for the Dominant Mode of Fibers with Various Noncircular Coresa

Equations (9)

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[ T 2 + k 2 ( r , θ ) β 2 ] φ ( r , θ ) = 0 ,
( r , θ ) = p = 0 N p ( r ) cos ( 2 p θ ) ,
φ ( r , θ ) = p = 0 N φ p ( r ) cos ( 2 p θ ) .
[ d 2 d r 2 + 1 r d d r + k 2 0 ( r ) β 2 ] φ 0 ( r ) + k 2 m = 1 N m ( r ) φ m ( r ) = 0 ,
[ d 2 d r 2 + 1 r d d r + k 2 0 ( r ) β 2 4 q 2 r 2 ] φ q ( r ) + k 2 2 ( m = 1 q m φ q m + m = q N m φ m q + m = 1 N q m φ m + q ) = 0 ( q = 1 , 2 , N ) .
φ p ( r ) = A p J p ( α r ) for r < R 1 ,
φ p ( r ) = B p K p ( γ r ) for r > R 2 ,
φ p ( r ) = B p K p ( γ r ) + C p I p ( γ r ) .
q = 0 N T pq ( β ) A q = 0 ( p = 0 , 1 ,… N ) .

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