Abstract

A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its p-1/p Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical results are compared with those obtained with other variants of the BPM.

© 2002 Optical Society of America

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2001 (2)

P. L. Ho and Y. Y. Lu, IEEE Photon. Technol. Lett. 13, 1316 (2001).
[CrossRef]

Q. Luo and C. T. Law, Opt. Lett. 26, 1708 (2001).
[CrossRef]

2000 (3)

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

D. Yevick and D. J. Thomson, J. Acoust. Soc. Am. 108, 2784 (2000).
[CrossRef]

1999 (1)

O. A. Godin, Wave Motion 29, 175 (1999).
[CrossRef]

1998 (2)

L. Poladian and F. Ladouceur, IEEE Photon. Tech. Lett. 10, 105 (1998).
[CrossRef]

Y. Y. Lu, Appl. Numer. Math. 27, 141 (1998).
[CrossRef]

1997 (4)

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, J. Acoust. Soc. Am. 101, 760 (1997).
[CrossRef]

C. Vassallo, Electron. Lett. 33, 61 (1997).
[CrossRef]

H. J. W. M. Hoekstra, Opt. Quant. Electron. 29, 157 (1997).
[CrossRef]

Y.-P. Chiou and H.-C. Chang, Opt. Lett. 22, 949 (1997).
[CrossRef] [PubMed]

1996 (2)

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

C. Vassallo and F. Collino, J. Lightwave Technol. 14, 1570 (1996).
[CrossRef]

1994 (1)

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

1993 (2)

M. D. Collins, J. Acoust. Soc. Am. 94, 975 (1993).
[CrossRef]

M. D. Collins, J. Acoust. Soc. Am. 93, 1736 (1993).
[CrossRef]

1992 (2)

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

G. R. Hadley, Opt. Lett. 17, 1743 (1992).
[CrossRef] [PubMed]

1991 (1)

1978 (1)

Brooke, G. H.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, J. Acoust. Soc. Am. 101, 760 (1997).
[CrossRef]

Chang, H.-C.

Chaudhuri, S.

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

Chiou, Y.-P.

Chu, S.

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

Collino, F.

C. Vassallo and F. Collino, J. Lightwave Technol. 14, 1570 (1996).
[CrossRef]

Collins, M. D.

M. D. Collins, J. Acoust. Soc. Am. 93, 1736 (1993).
[CrossRef]

M. D. Collins, J. Acoust. Soc. Am. 94, 975 (1993).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Godin, O. A.

O. A. Godin, Wave Motion 29, 175 (1999).
[CrossRef]

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

Hadley, G. R.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

Ho, P. L.

P. L. Ho and Y. Y. Lu, IEEE Photon. Technol. Lett. 13, 1316 (2001).
[CrossRef]

Hoekstra, H. J. W. M.

H. J. W. M. Hoekstra, Opt. Quant. Electron. 29, 157 (1997).
[CrossRef]

Huang, W.

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

Ladouceur, F.

L. Poladian and F. Ladouceur, IEEE Photon. Tech. Lett. 10, 105 (1998).
[CrossRef]

Law, C. T.

Lu, Y. Y.

P. L. Ho and Y. Y. Lu, IEEE Photon. Technol. Lett. 13, 1316 (2001).
[CrossRef]

Y. Y. Lu, Appl. Numer. Math. 27, 141 (1998).
[CrossRef]

Luo, Q.

Milinazzo, F. A.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, J. Acoust. Soc. Am. 101, 760 (1997).
[CrossRef]

Osgood, R. M.

Poladian, L.

L. Poladian and F. Ladouceur, IEEE Photon. Tech. Lett. 10, 105 (1998).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

R. Scarmozzino and R. M. Osgood, J. Opt. Soc. Am. A 8, 724 (1991).
[CrossRef]

Thomson, D. J.

D. Yevick and D. J. Thomson, J. Acoust. Soc. Am. 108, 2784 (2000).
[CrossRef]

Vassallo, C.

C. Vassallo, Electron. Lett. 33, 61 (1997).
[CrossRef]

C. Vassallo and F. Collino, J. Lightwave Technol. 14, 1570 (1996).
[CrossRef]

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

Xu, C.

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

Yevick, D.

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

D. Yevick and D. J. Thomson, J. Acoust. Soc. Am. 108, 2784 (2000).
[CrossRef]

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

Zala, C. A.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, J. Acoust. Soc. Am. 101, 760 (1997).
[CrossRef]

Appl. Numer. Math. (1)

Y. Y. Lu, Appl. Numer. Math. 27, 141 (1998).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

C. Vassallo, Electron. Lett. 33, 61 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, IEEE J. Sel. Top. Quantum Electron. 6, 150 (2000).
[CrossRef]

IEEE Photon. Tech. Lett. (1)

L. Poladian and F. Ladouceur, IEEE Photon. Tech. Lett. 10, 105 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

P. L. Ho and Y. Y. Lu, IEEE Photon. Technol. Lett. 13, 1316 (2001).
[CrossRef]

J. Acoust. Soc. Am. (4)

D. Yevick and D. J. Thomson, J. Acoust. Soc. Am. 108, 2784 (2000).
[CrossRef]

M. D. Collins, J. Acoust. Soc. Am. 94, 975 (1993).
[CrossRef]

M. D. Collins, J. Acoust. Soc. Am. 93, 1736 (1993).
[CrossRef]

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, J. Acoust. Soc. Am. 101, 760 (1997).
[CrossRef]

J. Lightwave Technol. (2)

W. Huang, C. Xu, S. Chu, and S. Chaudhuri, J. Lightwave Technol. 10, 295 (1992).
[CrossRef]

C. Vassallo and F. Collino, J. Lightwave Technol. 14, 1570 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (3)

Opt. Quant. Electron. (1)

H. J. W. M. Hoekstra, Opt. Quant. Electron. 29, 157 (1997).
[CrossRef]

Opt. Quantum Electron. (1)

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

Wave Motion (1)

O. A. Godin, Wave Motion 29, 175 (1999).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Absolute values of (solid curve) Pλ and (dotted curve) R7,8λ for s=5.

Fig. 2
Fig. 2

“Exact” solution (u2 at z=105) of Eq. (5) (denoted by the solid curves) compared with (a) solution by R7,8 (denoted by ° and (b) solution by R8,8.

Tables (1)

Tables Icon

Table 1 Relative Errors of ux,105 Calculated by Various Rational Approximants

Equations (13)

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

uzz+uxx+k02n2u=0,
n2n-2uzz+n2n-2uxx+k02n2u=0,
uz=ik0n*1+Xu,
X=k0n*-2x2+k02n2-k02n*2,X=k0n*-2n2xn-2x+k02n2-k02n*2
ϕz=ik0n*1+Xϕ, ϕ=1+X1/4u.
ϕz=ik0n*1n1+Xnϕ, ϕ=1n1+X1/4u.
uj+1=Puj, P=expis1+X,
ϕj+1=expisn-11+Xnϕj=1nexpis1+Xnϕj,
PRp,p=expisk=1p1+ckX1+bkX=expis1+k=1pakX1+bkX,
uj+1expisuj+k=1pakvk, 1+bkXvk=Xuj.
PRp-1,p=k=1pak1+bkX,
uj+1=k=1pakvk, 1+bkXvk=uj.
dz=1, z0; dz=0.5, zL=100.

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