Abstract

In the most current beam-propagation method (BPM), the coupling between the transverse and the longitudinal fields in z-dependent structures is ignored under the staircase approximation, which results in violation of power conservation. We propose a novel BPM that is derived in a local oblique coordinate system to analyze z-dependent structures accurately and efficiently without taking the staircase approximation. The coupling between the transverse and the longitudinal fields is automatically included in the local oblique coordinate system, and power is thus conserved if the reflection is neglected.

© 1998 Optical Society of America

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References

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  1. D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
    [CrossRef]
  2. G. R. Hadley, Opt. Lett. 17, 1426 (1992).
    [CrossRef]
  3. Y. P. Chiou and H. C. Chang, in 11th International Conference on Integrated Optics and Optical Fibre Communication (Institution of Electrical Engineers, London, 1997), Vol. 2, p. 19.
  4. J. Yamamuchi, J. Shibayama, and H. Nakano, in Integrated Photonics Research, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 19.
  5. P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
    [CrossRef]
  6. C. Vassallo, J. Opt. Soc. Am. A 13, 761 (1996).
    [CrossRef]
  7. P. Danielsen and D. Yevick, J. Opt. Commun. 4, 94 (1983).
    [CrossRef]
  8. C. Vassallo and F. Collino, J. Lightwave Technol. 15, 1958 (1997).
    [CrossRef]

1997

C. Vassallo and F. Collino, J. Lightwave Technol. 15, 1958 (1997).
[CrossRef]

1996

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

C. Vassallo, J. Opt. Soc. Am. A 13, 761 (1996).
[CrossRef]

1994

D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
[CrossRef]

1992

1983

P. Danielsen and D. Yevick, J. Opt. Commun. 4, 94 (1983).
[CrossRef]

Anada, T.

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

Benson, T. M.

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

Chang, H. C.

Y. P. Chiou and H. C. Chang, in 11th International Conference on Integrated Optics and Optical Fibre Communication (Institution of Electrical Engineers, London, 1997), Vol. 2, p. 19.

Chiou, Y. P.

Y. P. Chiou and H. C. Chang, in 11th International Conference on Integrated Optics and Optical Fibre Communication (Institution of Electrical Engineers, London, 1997), Vol. 2, p. 19.

Collino, F.

C. Vassallo and F. Collino, J. Lightwave Technol. 15, 1958 (1997).
[CrossRef]

Danielsen, P.

P. Danielsen and D. Yevick, J. Opt. Commun. 4, 94 (1983).
[CrossRef]

Hadley, G. R.

Kendall, P. C.

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

Nakano, H.

J. Yamamuchi, J. Shibayama, and H. Nakano, in Integrated Photonics Research, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 19.

Sewell, P.

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

Shibayama, J.

J. Yamamuchi, J. Shibayama, and H. Nakano, in Integrated Photonics Research, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 19.

Vassallo, C.

C. Vassallo and F. Collino, J. Lightwave Technol. 15, 1958 (1997).
[CrossRef]

C. Vassallo, J. Opt. Soc. Am. A 13, 761 (1996).
[CrossRef]

Yamamuchi, J.

J. Yamamuchi, J. Shibayama, and H. Nakano, in Integrated Photonics Research, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 19.

Yevick, D.

D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
[CrossRef]

P. Danielsen and D. Yevick, J. Opt. Commun. 4, 94 (1983).
[CrossRef]

J. Lightwave Technol.

C. Vassallo and F. Collino, J. Lightwave Technol. 15, 1958 (1997).
[CrossRef]

J. Opt. Commun.

P. Danielsen and D. Yevick, J. Opt. Commun. 4, 94 (1983).
[CrossRef]

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, Microwave Opt. Technol. Lett. 13, 24 (1996); J. Lightwave Technol. 13, 688 (1997).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
[CrossRef]

Other

Y. P. Chiou and H. C. Chang, in 11th International Conference on Integrated Optics and Optical Fibre Communication (Institution of Electrical Engineers, London, 1997), Vol. 2, p. 19.

J. Yamamuchi, J. Shibayama, and H. Nakano, in Integrated Photonics Research, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), p. 19.

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Figures (3)

Fig. 1
Fig. 1

Sampled points near the interface T.

Fig. 2
Fig. 2

Normalized power variation as the guided mode propagates along the curved waveguide.

Fig. 3
Fig. 3

Field distributions of the guided mode after it propagates (a) z = 4000 sin 60° µm and (b) z = 25 sin 60° µm. Dashed curves, theoretical results; solid curves, results calculated with the LOC BPM. The thick and the thin curves are the field-intensity amplitude and its corresponding real part, respectively. The oscillating behavior of the real parts accounts for the transverse phase difference.

Tables (1)

Tables Icon

Table 1 Field-Distribution Error

Equations (7)

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

ξ=x-z tan θ, ζ=z,
Ex,z=Φx,zexp-jk0n¯z cos θ+x sin θ
2z2+2x2-2jk0n¯cos θz+sin θx+k02n2x,z-n¯2Φx,z=0,
2ζ2+sec2 θ2ξ2-2jk0n¯ cos θζ-2 tan θ2ξζ+k02n2ξ-n¯2Φξ,ζ=0.
MmsΦms=Mms-1Φms-1L,
MmsHmsEms=Mms-1Hms-1Ems-1L,
PsEs=Ps-1Es-1G

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