Abstract

We present details of a simple method, incorporating first-order perturbation theory, to analyze the birefringence exhibited by elliptical-core fibers by using an equivalent rectangular-core waveguide. The results from this method are compared with those obtained from the finite-element and another approximate technique to demonstrate the accuracy of this simple method. The method may be extended to analyze waveguides of arbitrary geometry.

© 1989 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 Microwave Research Institute Symposium on Submillimeter Waves, J. Fox, ed. (Polytechnic, New York, 1970), p. 497.
  3. C. Yeh, K. Ha, S. B. Dong, W. P. Brown, Appl. Opt. 18, 1490 (1979).
    [CrossRef] [PubMed]
  4. K. L. Rajendra, R. V. Ramaswamy, IEEE J. Quantum Electron. QE-22, 986 (1986).
  5. A. Kumar, K. Thyagarajan, A. K. Ghatak, Opt. Lett. 8, 63 (1983).
    [CrossRef] [PubMed]
  6. A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
    [CrossRef]
  7. D. F. Clark, I. Dunlop, Electron. Lett. 24, 1414 (1988).
    [CrossRef]
  8. D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
    [CrossRef]

1988 (1)

D. F. Clark, I. Dunlop, Electron. Lett. 24, 1414 (1988).
[CrossRef]

1986 (1)

K. L. Rajendra, R. V. Ramaswamy, IEEE J. Quantum Electron. QE-22, 986 (1986).

1984 (1)

A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
[CrossRef]

1983 (1)

1979 (2)

C. Yeh, K. Ha, S. B. Dong, W. P. Brown, Appl. Opt. 18, 1490 (1979).
[CrossRef] [PubMed]

D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
[CrossRef]

1969 (1)

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

Brown, W. P.

Clark, D. F.

D. F. Clark, I. Dunlop, Electron. Lett. 24, 1414 (1988).
[CrossRef]

Cozens, J. R.

D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
[CrossRef]

Dong, S. B.

Dunlop, I.

D. F. Clark, I. Dunlop, Electron. Lett. 24, 1414 (1988).
[CrossRef]

Dyott, D.

D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
[CrossRef]

Ghatak, A. K.

Ha, K.

Knox, R. M.

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

Kumar, A.

A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
[CrossRef]

A. Kumar, K. Thyagarajan, A. K. Ghatak, Opt. Lett. 8, 63 (1983).
[CrossRef] [PubMed]

Marcatili, E. A. J.

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

Morris, D. G.

D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
[CrossRef]

Rajendra, K. L.

K. L. Rajendra, R. V. Ramaswamy, IEEE J. Quantum Electron. QE-22, 986 (1986).

Ramaswamy, R. V.

K. L. Rajendra, R. V. Ramaswamy, IEEE J. Quantum Electron. QE-22, 986 (1986).

Thyagarajan, K.

A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
[CrossRef]

A. Kumar, K. Thyagarajan, A. K. Ghatak, Opt. Lett. 8, 63 (1983).
[CrossRef] [PubMed]

Toulios, P. P.

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

Varshney, R. K.

A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
[CrossRef]

Yeh, C.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

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

Electron. Lett. (3)

A. Kumar, K. Thyagarajan, R. K. Varshney, Electron. Lett. 20, 112 (1984).
[CrossRef]

D. F. Clark, I. Dunlop, Electron. Lett. 24, 1414 (1988).
[CrossRef]

D. Dyott, J. R. Cozens, D. G. Morris, Electron. Lett. 15, 380 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. L. Rajendra, R. V. Ramaswamy, IEEE J. Quantum Electron. QE-22, 986 (1986).

Opt. Lett. (1)

Other (1)

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

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Figures (2)

Fig. 1
Fig. 1

Elliptical and rectangular waveguide geometry.

Fig. 2
Fig. 2

Comparison between the finite-element method8 (the solid curves), the perturbation analysis6 (the dashed curves), and the present analysis (the dotted curves).

Equations (9)

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β 1 2 = β 0 2 + k 0 2 Δ ( x , y ) | ψ ( x , y ) | 2 d x d y | ψ ( x , y ) | 2 d x d y ,
n 2 ( x , y ) = n 2 ( x ) + n 2 ( y ) n 1 2 ,
n ( x ) 2 = n 1 2 for | x | < a / 2 = n 2 2 for | x | > a / 2
n ( y ) 2 = n 1 2 for | y | < b / 2 = n 2 2 for | y | > b / 2 .
ψ ( x ) = A 1 cos ( γ 1 x x + α ) for | x | < a / 2 = A 2 exp ( γ 2 x | x | ) for | x | < a / 2
ψ ( y ) = B 1 cos ( γ 1 y y + ϕ ) for | y | < b / 2 = B 2 exp ( γ 2 y | y | ) for | y | < b / 2 .
A 2 A 1 = C 1 cos [ ( γ 1 x a / 2 ) + α ] exp ( γ 2 x a / 2 )
B 2 B 1 = n 1 2 n 2 2 1 C 1 cos [ ( γ 1 y b / 2 ) + ϕ ] exp ( γ 2 y b / 2 ) ,
area 3 cos 2 ( γ 1 x x ) ( B 2 B 1 ) 2 exp ( 2 γ 2 y y ) d x d y + area 1 exp ( 2 γ 2 x x ) ( A 2 A 1 ) 2 cos 2 ( γ 1 y y ) d x d y = area 2 cos 2 ( γ 1 x x ) cos 2 ( γ 1 y y ) d x d y .

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