Abstract

A method is proposed that allows for significant improvement of the numerical efficiency of the standard finite difference beam propagation algorithm. The advantages of the proposed method derive from the fact that it allows for an arbitrary selection of the preferred direction of propagation. It is demonstrated that such flexibility is particularly useful when studying the properties of obliquely propagating optical beams. The results obtained show that the proposed method achieves the same level of accuracy as the standard finite difference beam propagation method but with lower order Padé approximations and a coarser finite difference mesh.

© 2008 Optical Society of America

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  1. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
    [CrossRef]
  2. G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426-1428 (1992).
    [CrossRef] [PubMed]
  3. 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).
  4. C. Vassallo, “Limitations of the wide angle beam propagation method in nonuniform systems,” J. Opt. Soc. Am. A 13, 761-770 (1996).
    [CrossRef]
  5. D. Yevick, “The application of complex Padé approximants to vector field propagation,” IEEE Photon. Technol. Lett. 12, 1636-1638 (2000).
    [CrossRef]
  6. G. R. Hadley, “Multistep method for wide-angle beam propagation,” Opt. Lett. 17, 1743-1745 (1992).
    [CrossRef] [PubMed]
  7. H. J. W. M. Hoekstra, G. J. M. Krijnen, and P. V. Lambeck, “On the accuracy of the finite difference method for applications in beam propagation techniques,” Opt. Commun. 94, 506-508(1992).
    [CrossRef]
  8. D. Yevick, “Physics and simulation of optoelectronic devices,” Proc. SPIE 1679, 37-45 (1992).
    [CrossRef]
  9. I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modelling of waveguiding circuits,” J. Lightwave Technol. 14, 2813-2822 (1996).
    [CrossRef]
  10. C. Vassallo, “Interest of improved three-point formulas for finite-difference modelling of optical devices,” J. Opt. Soc. Am. A 14, 3273-3284 (1997).
    [CrossRef]
  11. D. Yevick and B. Hermansson, “Convergence properties of wide-angle techniques,” IEEE Photon. Technol. Lett. 6, 1457-1459 (1994).
    [CrossRef]
  12. G. R. Hadley, “Low truncation error finite difference equations for photonics simulation I: beam propagation,” J. Lightwave Technol. 16, 134-141 (1998).
    [CrossRef]
  13. J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
    [CrossRef]
  14. M. Koshiba and Y. Tsuji, “A wide-angle finite-element beam propagation method,” IEEE Photon. Technol. Lett. 8, 1208-1210 (1996).
    [CrossRef]
  15. C. C. Huang and C. C. Huang, “A novel wide-angle beam propagation method based on the spectral collocation scheme for computing tilted waveguides,” IEEE Photon. Technol. Lett. 17, 1872-1874 (2005).
    [CrossRef]
  16. I. Deshmukh and Q. H. Liu, “Pseudospectral beam-propagation method for optical waveguides,” IEEE Photonics Technol. Lett. 15, 60-62 (2003).
    [CrossRef]
  17. S. F. Helfert and R. Pregla, “Finite difference expressions for arbitrarily positioned dielectric steps in waveguide structures,” J. Lightwave Technol. 14, 2414-2421 (1996).
  18. D. Z. Djurdjevic, T. M. Benson, P. Sewell, and A. Vukovic, “Fast and accurate analysis of 3-D curved optical waveguide couplers,” J. Lightwave Technol. 22, 2333-2340 (2004).
    [CrossRef]
  19. S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
    [CrossRef]
  20. T. M. Benson, P. Sewell, S. Sujecki, and P. C. Kendall, “Structure related beam propagation,” Opt. Quantum Electron. 31, 689-793 (1999).
    [CrossRef]
  21. G. R. Hadley, “Slanted-wall beam propagation,” J. Lightwave Technol. 25, 2367-2375 (2007).
    [CrossRef]
  22. J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).
  23. P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
    [CrossRef]
  24. P. Sewell, T. M. Benson, T. Anada, and P. C. Kendall, “Bi-oblique propagation analysis of symmetric and asymmetric Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
    [CrossRef]
  25. S. Sujecki, “Wide-angle, finite difference beam propagation in oblique coordinate system,” J. Opt. Soc. Am. A 25, 138-145(2008).
    [CrossRef]
  26. P. Sewell, T. M. Benson, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(1999).
    [CrossRef]
  27. S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
    [CrossRef]

2008

2007

2005

C. C. Huang and C. C. Huang, “A novel wide-angle beam propagation method based on the spectral collocation scheme for computing tilted waveguides,” IEEE Photon. Technol. Lett. 17, 1872-1874 (2005).
[CrossRef]

2004

2003

I. Deshmukh and Q. H. Liu, “Pseudospectral beam-propagation method for optical waveguides,” IEEE Photonics Technol. Lett. 15, 60-62 (2003).
[CrossRef]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

2000

D. Yevick, “The application of complex Padé approximants to vector field propagation,” IEEE Photon. Technol. Lett. 12, 1636-1638 (2000).
[CrossRef]

1999

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, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(1999).
[CrossRef]

S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
[CrossRef]

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

1998

1997

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

J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
[CrossRef]

C. Vassallo, “Interest of improved three-point formulas for finite-difference modelling of optical devices,” J. Opt. Soc. Am. A 14, 3273-3284 (1997).
[CrossRef]

1996

S. F. Helfert and R. Pregla, “Finite difference expressions for arbitrarily positioned dielectric steps in waveguide structures,” J. Lightwave Technol. 14, 2414-2421 (1996).

M. Koshiba and Y. Tsuji, “A wide-angle finite-element beam propagation method,” IEEE Photon. Technol. Lett. 8, 1208-1210 (1996).
[CrossRef]

I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modelling of waveguiding circuits,” J. Lightwave Technol. 14, 2813-2822 (1996).
[CrossRef]

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
[CrossRef]

C. Vassallo, “Limitations of the wide angle beam propagation method in nonuniform systems,” J. Opt. Soc. Am. A 13, 761-770 (1996).
[CrossRef]

1995

J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).

1994

D. Yevick and B. Hermansson, “Convergence properties of wide-angle techniques,” IEEE Photon. Technol. Lett. 6, 1457-1459 (1994).
[CrossRef]

1992

H. J. W. M. Hoekstra, G. J. M. Krijnen, and P. V. Lambeck, “On the accuracy of the finite difference method for applications in beam propagation techniques,” Opt. Commun. 94, 506-508(1992).
[CrossRef]

D. Yevick, “Physics and simulation of optoelectronic devices,” Proc. SPIE 1679, 37-45 (1992).
[CrossRef]

G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17, 1426-1428 (1992).
[CrossRef] [PubMed]

G. R. Hadley, “Multistep method for wide-angle beam propagation,” Opt. Lett. 17, 1743-1745 (1992).
[CrossRef] [PubMed]

1990

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

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 symmetric and asymmetric Y-junctions,” J. Lightwave Technol. 15, 688-696 (1997).
[CrossRef]

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
[CrossRef]

Benson, T. M.

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

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

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, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(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).

S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
[CrossRef]

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

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
[CrossRef]

Borruel, L.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Chung, Y.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

Dagli, N.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

Deshmukh, I.

I. Deshmukh and Q. H. Liu, “Pseudospectral beam-propagation method for optical waveguides,” IEEE Photonics Technol. Lett. 15, 60-62 (2003).
[CrossRef]

Djurdjevic, D. Z.

Erbert, G.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Esquivias, I.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Hadley, G. R.

Helfert, S. F.

S. F. Helfert and R. Pregla, “Finite difference expressions for arbitrarily positioned dielectric steps in waveguide structures,” J. Lightwave Technol. 14, 2414-2421 (1996).

Hermansson, B.

D. Yevick and B. Hermansson, “Convergence properties of wide-angle techniques,” IEEE Photon. Technol. Lett. 6, 1457-1459 (1994).
[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).

Hoekstra, H. J. W. M.

H. J. W. M. Hoekstra, G. J. M. Krijnen, and P. V. Lambeck, “On the accuracy of the finite difference method for applications in beam propagation techniques,” Opt. Commun. 94, 506-508(1992).
[CrossRef]

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).

Huang, C. C.

C. C. Huang and C. C. Huang, “A novel wide-angle beam propagation method based on the spectral collocation scheme for computing tilted waveguides,” IEEE Photon. Technol. Lett. 17, 1872-1874 (2005).
[CrossRef]

C. C. Huang and C. C. Huang, “A novel wide-angle beam propagation method based on the spectral collocation scheme for computing tilted waveguides,” IEEE Photon. Technol. Lett. 17, 1872-1874 (2005).
[CrossRef]

Ilic, I.

I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modelling of waveguiding circuits,” J. Lightwave Technol. 14, 2813-2822 (1996).
[CrossRef]

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, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(1999).
[CrossRef]

S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
[CrossRef]

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

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
[CrossRef]

Koshiba, M.

M. Koshiba and Y. Tsuji, “A wide-angle finite-element beam propagation method,” IEEE Photon. Technol. Lett. 8, 1208-1210 (1996).
[CrossRef]

Krijnen, G. J. M.

H. J. W. M. Hoekstra, G. J. M. Krijnen, and P. V. Lambeck, “On the accuracy of the finite difference method for applications in beam propagation techniques,” Opt. Commun. 94, 506-508(1992).
[CrossRef]

Lambeck, P. V.

H. J. W. M. Hoekstra, G. J. M. Krijnen, and P. V. Lambeck, “On the accuracy of the finite difference method for applications in beam propagation techniques,” Opt. Commun. 94, 506-508(1992).
[CrossRef]

Larkins, E. C.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Liu, Q. H.

I. Deshmukh and Q. H. Liu, “Pseudospectral beam-propagation method for optical waveguides,” IEEE Photonics Technol. Lett. 15, 60-62 (2003).
[CrossRef]

Moreno, P.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Nakano, H.

J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).

Osgood, R. M.

I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modelling of waveguiding circuits,” J. Lightwave Technol. 14, 2813-2822 (1996).
[CrossRef]

Pregla, R.

S. F. Helfert and R. Pregla, “Finite difference expressions for arbitrarily positioned dielectric steps in waveguide structures,” J. Lightwave Technol. 14, 2414-2421 (1996).

Scarmozzino, R.

I. Ilić, R. Scarmozzino, and R. M. Osgood, “Investigation of the Padé approximant-based wide-angle beam propagation method for accurate modelling of waveguiding circuits,” J. Lightwave Technol. 14, 2813-2822 (1996).
[CrossRef]

Sekiguchi, M.

J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
[CrossRef]

Sewell, P.

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

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

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, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(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).

S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
[CrossRef]

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

P. Sewell, T. Anada, T. M. Benson, and P. C. Kendall, “Non standard beam propagation,” Microw. Opt. Technol. Lett. 13, 24-26 (1996).
[CrossRef]

Shibayama, J.

J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).

Sujecki, S.

S. Sujecki, “Wide-angle, finite difference beam propagation in oblique coordinate system,” J. Opt. Soc. Am. A 25, 138-145(2008).
[CrossRef]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

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, S. Sujecki, and P. C. Kendall, “The dispersion characteristics of oblique coordinate beam propagation algorithms,” J. Lightwave Technol. 17, 514-518(1999).
[CrossRef]

S. Sujecki, P. Sewell, T. M. Benson, and P. C. Kendall, “Novel beam propagation algorithms for tapered optical structures,” J. Lightwave Technol. 17, 2379-2388 (1999).
[CrossRef]

Sumpf, B.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Tsuji, Y.

M. Koshiba and Y. Tsuji, “A wide-angle finite-element beam propagation method,” IEEE Photon. Technol. Lett. 8, 1208-1210 (1996).
[CrossRef]

Vassallo, C.

Vukovic, A.

Wenzel, H.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Wykes, J.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

Yamauchi, J.

J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, “Finite-difference beam propagation method based on the generalized Douglas scheme for nonuniform grid,” IEEE Photon. Technol. Lett. 9, 67-69 (1997).
[CrossRef]

J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).

Yevick, D.

D. Yevick, “The application of complex Padé approximants to vector field propagation,” IEEE Photon. Technol. Lett. 12, 1636-1638 (2000).
[CrossRef]

D. Yevick and B. Hermansson, “Convergence properties of wide-angle techniques,” IEEE Photon. Technol. Lett. 6, 1457-1459 (1994).
[CrossRef]

D. Yevick, “Physics and simulation of optoelectronic devices,” Proc. SPIE 1679, 37-45 (1992).
[CrossRef]

Electron. Commun. Jpn. 2, Electron.

J. Yamauchi, J. Shibayama, and H. Nakano, “Finite difference beam propagation method using the oblique coordinate system,” Electron. Commun. Jpn. 2, Electron. 78, 20-27(1995).

IEEE J. Quantum Electron.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, “Non-linear properties of tapered laser cavities,” IEEE J. Sel. Top. Quantum Electron. 9, 823 (2003).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of off-axis optical beam propagation; α denotes schematically the beam angular bandwidth

Fig. 2
Fig. 2

Dependence of the relative error in the z component of the wave vector on the propagation angle of the generalized rectangular BPM for (a) 1st order wide angle approximation, WA(1,1) and (b) 2nd order wide angle approximation, WA(2,2). The longitudinal and transverse mesh size is equal to 0.2 μm . The refractive index of the medium is 1, while the reference refractive index matches that of the medium.

Fig. 3
Fig. 3

Dependence of the relative error in the z component of the wave vector on the propagation angle of the generalized rectangular BPM for (a) 1st order wide angle approximation, WA(1,1) and (b) 2nd order wide angle approximation, WA(2,2). The longitudinal and transverse mesh size is equal to 0.01 μm . The refractive index of the medium is 1, while the reference refractive index matches that of the medium.

Fig. 4
Fig. 4

Intensity profiles resulting from the propagation of a 45 ° tilted plane wave with a Gaussian envelope through a distance of 10 μm along the z axis. The beam was propagated through a homogenous medium with refractive index equal to 1. The reference refractive index matches that of the medium. The longitudinal and transverse mesh size is 0.01 μm and 0.004 μm , respectively.

Fig. 5
Fig. 5

Intensity profiles resulting from the propagation of a 45 ° tilted plane wave with a Gaussian envelope through a distance of 10 μm along the z axis. The beam was propagated through a homogenous medium with refractive index equal to 1. The reference refractive index matches that of the medium. The longitudinal and transverse mesh size is equal to 0.2 μm .

Fig. 6
Fig. 6

Intensity profiles resulting from the propagation of a 45 ° tilted plane wave with a Gaussian envelope through a distance of 10 μm along the z axis. The beam was propagated through a homogenous medium with refractive index equal to 1. The reference refractive index matches that of the medium. 2nd order wide angle approximation was used.

Fig. 7
Fig. 7

Tilted waveguide structure.

Fig. 8
Fig. 8

Dependence of the field offset on the wide angle approximation order and preferred angle of propagation θ for the tilted waveguide structure from Fig. 7: d z = d x = (a)  0.05 μm and (b)  0.01 μm . The reference refractive index was equal to 3.262.

Tables (1)

Tables Icon

Table 1 CPU-Time Needed for Calculating the Field Intensity Profiles Shown in Fig. 5

Equations (8)

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2 Ψ z 2 + 2 Ψ x 2 + k 2 Ψ = 0 ,
Φ z = L ( 1 1 + M L 2 ) Φ ,
L = j β cos θ , M = k 2 β 2 + 2 t 2 2 j β sin θ t .
Φ z = ( 1 2 M L ) Φ ,
Φ z = i = 1 n a i , n L M L 2 + b i , n M Φ .
Φ ( z = z 0 + Δ z ) = exp ( i = 1 n a i , n L M L 2 1 + b i , n M L 2 ) Δ z Φ ( z = z 0 ) .
Φ ( z = z 0 + Δ z ) = i = 1 n exp ( a i , n L M L 2 + b i , n M ) Δ z Φ ( z = z 0 ) .
Φ ( z = z 0 + Δ z ) = i = 1 n L 2 + b i , n M Δ z 2 ( a i , n L M ) L 2 + b i , n M + Δ z 2 ( a i , n L M ) Φ ( z = z 0 .

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