Abstract

The vector coupled-mode analysis considering the exact HE11 modes is applied to two single-mode coupled optical fiber cores, including the strongly guiding fibers. The accuracy of the conventional coupled-mode theory and the recently formulated new theory as applied to the two-core system is examined. Array modes of different polarization states are considered. It is shown that the full-wave coupled-mode calculations behave well in predicting the array-mode propagation constants beyond the weakly guiding regime and that the simpler conventional theory can provide satisfactory results when applied in the vectorial form.

© 1989 Optical Society of America

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References

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  1. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
  2. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  3. A Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).
  4. W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).
  5. S. L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).
  6. H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).
  7. D. Gloge, Appl. Opt. 10, 2252 (1971).
  8. A. Hardy, S. Shakir, W. Streifer, Opt. Lett. 11, 324 (1986).
  9. A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).
  10. A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).
  11. A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).
  12. The conventional coupled-mode equations in Refs. 1 and 2, which appear to have interchanged coupling coefficients, were shown in Ref. 13 to be consistent with each other.
  13. H.-C. Chang, IEEE J. Quantum Electron. QE-23, 1929 (1987).
  14. H. S. Huang, H.-C. Chang, “Analysis of optical fiber directional coupling based on the HE11 modes,” submitted to IEEE J. Lightwave Technol.
  15. C. Vassallo, IEEE J. Lightwave Technol. LT-6, 294 (1988).
  16. W. Wijngaard, J. Opt. Soc. Am. 63, 944 (1973).

1988 (2)

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).

C. Vassallo, IEEE J. Lightwave Technol. LT-6, 294 (1988).

1987 (4)

H.-C. Chang, IEEE J. Quantum Electron. QE-23, 1929 (1987).

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).

S. L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

1986 (3)

A. Hardy, S. Shakir, W. Streifer, Opt. Lett. 11, 324 (1986).

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).

1985 (1)

A Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).

1973 (1)

1972 (1)

1971 (1)

Ankiewicz, A.

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).

Chang, H.-C.

H.-C. Chang, IEEE J. Quantum Electron. QE-23, 1929 (1987).

H. S. Huang, H.-C. Chang, “Analysis of optical fiber directional coupling based on the HE11 modes,” submitted to IEEE J. Lightwave Technol.

Chuang, S. L.

S. L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).

Gloge, D.

Hardy, A

A Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).

Hardy, A.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).

A. Hardy, S. Shakir, W. Streifer, Opt. Lett. 11, 324 (1986).

Haus, H. A.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

Huang, H. S.

H. S. Huang, H.-C. Chang, “Analysis of optical fiber directional coupling based on the HE11 modes,” submitted to IEEE J. Lightwave Technol.

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Osinski, M.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).

Shakir, S.

Snyder, A. W.

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).

A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Streifer, W.

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).

A. Hardy, S. Shakir, W. Streifer, Opt. Lett. 11, 324 (1986).

A Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).

Vassallo, C.

C. Vassallo, IEEE J. Lightwave Technol. LT-6, 294 (1988).

Whitaker, N. A.

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

Wijngaard, W.

Zheng, X.-H.

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).

Appl. Opt. (1)

Electron. Lett. (1)

A. W. Snyder, A. Ankiewicz, Electron. Lett. 22, 1237 (1986).

IEEE J. Lightwave Technol. (7)

A. W. Snyder, A. Ankiewicz, IEEE J. Lightwave Technol. LT-6, 463 (1988).

C. Vassallo, IEEE J. Lightwave Technol. LT-6, 294 (1988).

A. Ankiewicz, A. W. Snyder, X.-H. Zheng, IEEE J. Lightwave Technol. LT-4, 1317 (1986).

A Hardy, W. Streifer, IEEE J. Lightwave Technol. LT-3, 1135 (1985).

W. Streifer, M. Osinski, A. Hardy, IEEE J. Lightwave Technol. LT-5, 1 (1987).

S. L. Chuang, IEEE J. Lightwave Technol. LT-5, 5 (1987).

H. A. Haus, W. P. Huang, S. Kawakami, N. A. Whitaker, IEEE J. Lightwave Technol. LT-5, 16 (1987).

IEEE J. Quantum Electron. (1)

H.-C. Chang, IEEE J. Quantum Electron. QE-23, 1929 (1987).

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

H. S. Huang, H.-C. Chang, “Analysis of optical fiber directional coupling based on the HE11 modes,” submitted to IEEE J. Lightwave Technol.

The conventional coupled-mode equations in Refs. 1 and 2, which appear to have interchanged coupling coefficients, were shown in Ref. 13 to be consistent with each other.

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Figures (5)

Fig. 1
Fig. 1

Cross sections in the xy plane of a parallel identical-core system. (a) Tangent cores with D = 2a, (b) separated cores with D = 3a. V, the normalized frequency.

Fig. 2
Fig. 2

Normalized propagation constants versus nco (with ncl = 1.46 and λ = 1.3 μm) for the even and odd Ez-sine array modes for the case in Fig. 1(a) with three different V values. The solid curves are the exact values, the dotted curves correspond to the conventional theory, and the dashed curves correspond to the new theory. The crosses and circles represent the conventional and the new coupled-mode results, respectively, based on the LP01 modes.

Fig. 3
Fig. 3

Normalized propagation constants for the even and odd Ez-cosine array modes for the case in Fig. 1(a). The curves and symbols are the same as in Fig. 2.

Fig. 4
Fig. 4

Normalized propagation constants for the even and odd Ez-sine array modes for the case in Fig 1(b). The curves and symbols are the same as in Fig. 2.

Fig. 5
Fig. 5

Normalized propagation constants for the even and odd Ez-cosine array modes for the case in Fig. 1(b). The curves and symbols are the same as in Fig. 2.

Equations (2)

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b = ( β / k 0 ) 2 n cl 2 n co 2 n cl 2 ,
Δ β / β < ( Δ b ) n co 2 n cl 2 2 n cl 2 ,

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