Abstract

A low-truncation-error scheme for a step-index profile is applied to analysis of a three-dimensional waveguide with the aid of the alternating-direction implicit method. The propagation constants of a single and a coupled rib waveguide are analyzed by use of the imaginary distance procedure. A fast convergence rate, which is not obtainable with the conventional second-order schemes, is realized, leading to highly accurate evaluation of the coupling length. A reduction in discretization error is also demonstrated in the beam-propagation analysis of a tilted rib-waveguide coupler.

© 2000 Optical Society of America

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References

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2000 (2)

J. Yamauchi, S. Nakamura, and H. Nakano, IEEE Photon. Technol. Lett. 12, 1001 (2000).
[CrossRef]

Y-P. Chiou, Y.-C. Chiang, and H.-C. Chang, J. Lightwave Technol. 18, 243 (2000).
[CrossRef]

1999 (2)

1998 (3)

1997 (2)

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

C. Vassallo, Opt. Quantum Electron. 29, 95 (1997).
[CrossRef]

1996 (1)

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

1992 (2)

1989 (1)

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[CrossRef]

1988 (1)

M. S. Stern, IEE Proc. J 135, 333 (1988).

Chang, H.-C.

Chiang, Y.-C.

Chiou, Y-P.

Feit, M. D.

Fleck, J. A.

Hadley, G. R.

Hermansson, B.

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[CrossRef]

Matsubara, K.

Nakamura, S.

J. Yamauchi, S. Nakamura, and H. Nakano, IEEE Photon. Technol. Lett. 12, 1001 (2000).
[CrossRef]

Nakano, H.

J. Yamauchi, S. Nakamura, and H. Nakano, IEEE Photon. Technol. Lett. 12, 1001 (2000).
[CrossRef]

J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 17, 677 (1999).
[CrossRef]

J. Yamauchi, J. Shibayama, and H. Nakano, Opt. Quantum Electron. 31, 675 (1999).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, IEEE Photon. Technol. Lett. 10, 1127 (1998).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, J. Lightwave Technol. 16, 2458 (1998).
[CrossRef]

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

Ratowsky, R. P.

Saito, O.

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

Sekiguchi, M.

J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 17, 677 (1999).
[CrossRef]

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

Shibayama, J.

J. Yamauchi, J. Shibayama, and H. Nakano, Opt. Quantum Electron. 31, 675 (1999).
[CrossRef]

J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 17, 677 (1999).
[CrossRef]

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

Stern, M. S.

M. S. Stern, IEE Proc. J 135, 333 (1988).

Takahashi, G.

J. Yamauchi, G. Takahashi, and H. Nakano, IEEE Photon. Technol. Lett. 10, 1127 (1998).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, J. Lightwave Technol. 16, 2458 (1998).
[CrossRef]

Uchiyama, O.

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

Vassallo, C.

C. Vassallo, Opt. Quantum Electron. 29, 95 (1997).
[CrossRef]

C. Vassallo, IEE Proc. J 139, 137 (1992).

Yamauchi, J.

J. Yamauchi, S. Nakamura, and H. Nakano, IEEE Photon. Technol. Lett. 12, 1001 (2000).
[CrossRef]

J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 17, 677 (1999).
[CrossRef]

J. Yamauchi, J. Shibayama, and H. Nakano, Opt. Quantum Electron. 31, 675 (1999).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, IEEE Photon. Technol. Lett. 10, 1127 (1998).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, J. Lightwave Technol. 16, 2458 (1998).
[CrossRef]

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, O. Saito, O. Uchiyama, and H. Nakano, J. Lightwave Technol. 14, 2401 (1996).
[CrossRef]

Yevick, D.

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[CrossRef]

IEE Proc. J (2)

M. S. Stern, IEE Proc. J 135, 333 (1988).

C. Vassallo, IEE Proc. J 139, 137 (1992).

IEEE J. Quantum Electron. (1)

D. Yevick and B. Hermansson, IEEE J. Quantum Electron. 25, 221 (1989).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. Yamauchi, S. Nakamura, and H. Nakano, IEEE Photon. Technol. Lett. 12, 1001 (2000).
[CrossRef]

J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, IEEE Photon. Technol. Lett. 9, 961 (1997).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, IEEE Photon. Technol. Lett. 10, 1127 (1998).
[CrossRef]

J. Lightwave Technol. (5)

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

Opt. Quantum Electron. (2)

J. Yamauchi, J. Shibayama, and H. Nakano, Opt. Quantum Electron. 31, 675 (1999).
[CrossRef]

C. Vassallo, Opt. Quantum Electron. 29, 95 (1997).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometry of a rib waveguide.

Fig. 2
Fig. 2

Convergence behavior of the normalized propagation constant B of a rib waveguide as a function of transverse sampling width Δ: (a) quasi-TE mode, (b) quasi-TM mode. The modal transverse resonance method (MTRM) is from Ref. 10. See text for other definitions.

Fig. 3
Fig. 3

Geometry of a rib-waveguide coupler.

Fig. 4
Fig. 4

Convergence behavior of the propagation constants βeven and βodd for a rib-waveguide coupler as a function of Δ (quasi-TE mode).

Fig. 5
Fig. 5

Convergence behavior of coupling length Lc as a function of transverse sampling width Δ (quasi-TE mode).

Fig. 6
Fig. 6

Contour field plot of a tilted rib-waveguide coupler (quasi-TM mode): (a) present scheme, (b) staircase approximation.

Equations (2)

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

ζ1-f2-ζ2-f1ϕi-1,jl+1/2+ζ0-g1,2+ζ1-g2,0-ζ2-g1,0ϕi,jl+1/2+ζ2-e1-ζ1-e2ϕi+1,jl+1/2=ζ1+f2-ζ2+f1ϕi,j-1l+ζ0+g1,2+ζ1+g2,0-ζ2+g1,0ϕi,jlζ2+e1-ζ1+e2ϕi,j+1l,
gm,n=emfn-enfm,  ζm±=2jk0n0gm+2,1g2,1±Δz4k02ni,j2-n02gm+2,1g2,1+mm-1.

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