Abstract

We propose a novel beam-propagation method (BPM) based on the higher-order Padé approximants in both the transverse and the longitudinal directions. Extending the Padé approximation to the propagation direction and adopting the multistep method increase the programming effort by only a small amount. Compared with the conventional BPM's, this method is more accurate and efficient. The accuracy and the propagation step size are well predicted by a phase analysis.

© 1997 Optical Society of America

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References

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  1. N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
    [CrossRef]
  2. D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
    [CrossRef]
  3. P. L. Liu and B. J. Li, IEEE J. Quantum Electron. 29, 2385 (1993).
    [CrossRef]
  4. H. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
    [CrossRef]
  5. D. Yevick and M. Glasner, Opt. Lett. 15, 174 (1990).
    [CrossRef] [PubMed]
  6. G. R. Hadley, Opt. Lett. 17, 1426 (1992).
    [CrossRef]
  7. Y. Chung and N. Dagli, IEEE Photon. Technol. Lett. 6, 540 (1994).
    [CrossRef]
  8. D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
    [CrossRef]
  9. G. R. Hadley, Opt. Lett. 17, 1743 (1992).
    [CrossRef] [PubMed]
  10. G. A. Baker, Essentials of Padé Approximants (Academic, New York, 1975).

1994 (2)

Y. Chung and N. Dagli, IEEE Photon. Technol. Lett. 6, 540 (1994).
[CrossRef]

D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
[CrossRef]

1993 (2)

P. L. Liu and B. J. Li, IEEE J. Quantum Electron. 29, 2385 (1993).
[CrossRef]

H. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

1992 (2)

1990 (2)

D. Yevick and M. Glasner, Opt. Lett. 15, 174 (1990).
[CrossRef] [PubMed]

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[CrossRef]

1976 (1)

N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Baker, G. A.

G. A. Baker, Essentials of Padé Approximants (Academic, New York, 1975).

Chung, Y.

Y. Chung and N. Dagli, IEEE Photon. Technol. Lett. 6, 540 (1994).
[CrossRef]

Dagli, N.

Y. Chung and N. Dagli, IEEE Photon. Technol. Lett. 6, 540 (1994).
[CrossRef]

Feit, M. D.

N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleck, N. A.

N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Glasner, M.

Glingener, C.

D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
[CrossRef]

Hadley, G. R.

Hermansson, B.

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[CrossRef]

Huang, H. P.

H. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Li, B. J.

P. L. Liu and B. J. Li, IEEE J. Quantum Electron. 29, 2385 (1993).
[CrossRef]

Liu, P. L.

P. L. Liu and B. J. Li, IEEE J. Quantum Electron. 29, 2385 (1993).
[CrossRef]

Morris, J. R.

N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Schulz, D.

D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
[CrossRef]

Voges, E.

D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
[CrossRef]

Xu, C. L.

H. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Yevick, D.

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[CrossRef]

D. Yevick and M. Glasner, Opt. Lett. 15, 174 (1990).
[CrossRef] [PubMed]

Appl. Phys. (1)

N. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

IEEE J. Quantum Electron. (4)

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 26, 109 (1990).
[CrossRef]

P. L. Liu and B. J. Li, IEEE J. Quantum Electron. 29, 2385 (1993).
[CrossRef]

H. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

D. Schulz, C. Glingener, and E. Voges, IEEE J. Quantum Electron. 30, 1132 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Chung and N. Dagli, IEEE Photon. Technol. Lett. 6, 540 (1994).
[CrossRef]

Opt. Lett. (3)

Other (1)

G. A. Baker, Essentials of Padé Approximants (Academic, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Relation between the relative phase error and the normalized step.

Fig. 2
Fig. 2

Power variation in waveguide a of the directional coupler shown as the inset: paraxial cases.

Fig. 3
Fig. 3

Power variation in waveguide a of the directional coupler shown as the inset:  WA cases.

Equations (17)

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2Etz2+t2Et+k02n2Et+ttn2n2Et=0,
d2Φdz2+LΦ=0,
Φz0+Δz=exp-jLΔzΦz0.
exp-jLΔz=V-1 exp-jΛΔzV
ddz=L-k02n¯22jk0n¯-ddzP,
dϕzdz=Pϕz.
ϕz+Δz=2D-jΔzND+jΔzNϕz,
ϕz+Δz=expPΔzϕzexpηϕz.
Pz10η=1+η,
Pz11η=2+η/2-η,
Pz22η=12+6η+η2/12-6η+η2,
Pz33η=120+60η+12η2+η3/120-60η+12η2-η3.
expη=Pzpqη+Oηp+q+1.
ϕz+Δz=i=0pr1+ciLi=0pr1+ci*Lϕz,
ϕi+1/pr=1+ciL1+ci*Lϕi/pr,
ζN/DΔz.
ζ=ϕcalculated-ζζ,

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