Abstract

A fast and efficient three-dimensional generalized rectangular wide-angle beam propagation method (GR-WA-BPM) based on a recently proposed modified Padé (1,1) approximant is presented. In our method, at each propagation step, the beam propagation equation is recast in terms of a Helmholtz equation with a source term, which is solved quickly and accurately by a recently introduced complex Jacobi iterative (CJI) method. The efficiency of the GR-WA-BPM for the analysis of tilted optical waveguides is demonstrated in comparison with the standard wide-angle beam propagation method based on Hadley’s scheme. In addition, since the utility of the CJI method depends mostly on its execution speed in comparison with the traditional direct matrix inversion, several performance comparisons are also presented.

© 2009 Optical Society of America

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References

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  1. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2009 (1)

K. Q. Le, “Complex Padé approximant operators for wide-angle beam propagation,” Opt. Commun. 282, 1252-1254 (2009).
[CrossRef]

2008 (3)

2007 (1)

2004 (1)

2000 (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

1999 (2)

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
[CrossRef]

1997 (2)

P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetry and assymetry Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, “Rational square root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760-766 (1997).
[CrossRef]

1992 (2)

Anada, T.

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetry and assymetry Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

Benson, T. M.

D. Z. Djurdjevic, T. M. Benson, P. Sewell, and A. Vukovic, “Fast and accurate analysis of 3D curved optical waveguide couplers,” J. Lightwave Technol. 22, 2333-2340 (2004).
[CrossRef]

T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
[CrossRef]

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetry and assymetry Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

Bienstman, P.

Brooke, G. H.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, “Rational square root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760-766 (1997).
[CrossRef]

Djurdjevic, D. Z.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

Hadley, G. R.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

Hiraoka, T.

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

Hokazono, T.

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

Hsu, J. P.

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

Kendall, P. C.

T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
[CrossRef]

P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetry and assymetry Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

Le, K. Q.

Milinazzo, F. A.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, “Rational square root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760-766 (1997).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

Rubio, R. G.

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

Sewell, P.

D. Z. Djurdjevic, T. M. Benson, P. Sewell, and A. Vukovic, “Fast and accurate analysis of 3D curved optical waveguide couplers,” J. Lightwave Technol. 22, 2333-2340 (2004).
[CrossRef]

T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
[CrossRef]

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetry and assymetry Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

Sujecki, S.

Vukovic, A.

Zala, C. A.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, “Rational square root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760-766 (1997).
[CrossRef]

Appl. Opt. (1)

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

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-161 (2000).
[CrossRef]

IEICE Trans. Electron. (1)

T. Anada, T. Hokazono, T. Hiraoka, J. P. Hsu, T. M. Benson, and P. Sewell, “Very-wide-angle beam propagation methods for integrated optical circuits,” IEICE Trans. Electron. E82-C, 1154-1158 (1999).

J. Acoust. Soc. Am. (1)

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, “Rational square root approximations for parabolic equation algorithms,” J. Acoust. Soc. Am. 101, 760-766 (1997).
[CrossRef]

J. Lightwave Technol. (3)

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

Opt. Commun. (1)

K. Q. Le, “Complex Padé approximant operators for wide-angle beam propagation,” Opt. Commun. 282, 1252-1254 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Intensity profiles along a tilted WG for (a) the standard and (b) the generalized rectangular wide-angle propagations.

Fig. 2
Fig. 2

Intensity peaks along a tilted WG for the standard (dotted curve) and the generalized rectangular (solid curve) wide-angle propagations.

Fig. 3
Fig. 3

Magnitude of 3D Gaussian beam after propagating 1 μ m calculated by the generalized rectangular WA-BPM based on (a) DMI and (b) CJI.

Tables (1)

Tables Icon

Table 1 Quantitative Comparison of Runtimes (in seconds) of the DMI and CJI methods for GR-WA Beam Propagation in WG Structures

Equations (12)

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2 Ψ x 2 + 2 Ψ y 2 + 2 Ψ z 2 + k 0 2 n 2 ( x , y , z ) Ψ = 0 ,
Ψ ( x , y , z ) = Φ ( x , y , z ) exp [ i k   cos ( θ ) z + i k   sin ( θ ) x ] ,
2 Φ z 2 + 2 j k   cos   θ Φ z + P Φ = 0 ,
P = 2 y 2 + 2 x 2 + 2 j k   sin   θ x + k 0 2 ( n 2 n ref 2 ) .
Φ z j 2 k   cos   θ 2 Φ z 2 = j P 2 k   cos   θ Φ ,
Φ z = i P 2 k   cos   θ 1 i 2 k   cos   θ z Φ .
| z | n + 1 = i P 2 k   cos   θ 1 i 2 k   cos   θ | z | n Φ .
Φ z i k   cos ( θ ) N ( m ) D ( n ) Φ ,
D ( Φ n + 1 Φ n ) = i k   cos ( θ ) Δ z 2 N ( Φ n + 1 + Φ n ) .
( 1 + ξ P ) Φ n + 1 = ( 1 + ξ P ) Φ n ,
[ 2 y 2 + 2 x 2 + 2 j k   sin   θ x + k 0 2 ( n 2 n ref 2 ) + 1 ξ ] Φ n + 1 = ( ξ ξ P + 1 ξ ) Φ n
[ 2 y 2 + 2 x 2 + 2 j k   sin   θ x + k 0 2 ( n 2 n ref 2 ) + 1 ξ ] Φ n + 1 = source   term .

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