Abstract

In recent years the finite-element method (FEM) has been widely applied to three-dimensional beam propagation analysis, and several FEM propagators have been presented. Up to now, as far as we know, an exhaustive, deep, and comparative analysis of these formulations and of the related algorithms has never been presented. We critically analyze and numerically compare, to our knowledge for the first time, different vectorial, semivectorial, and scalar formulations in order to check their performances, point out weaknesses, and suggest future developments. The results obtained highlight once more the inadequacy of scalar approaches in dealing with actual photonics devices and suggest vector formulations worthy of further development and future research.

© 2000 Optical Society of America

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  1. J. Van Roey, J. Van der Donk, P. Lagasse, “Beam propagation method: analysis and assessment,” J. Opt. Soc. Am. 71, 803–810 (1981).
    [CrossRef]
  2. H. E. Hernandez-Figueroa, “Efficient 3-D split operator finite element algorithm for scalar integrated optics,” IEEE Photon. Technol. Lett. 9, 351–353 (1997).
    [CrossRef]
  3. Y. Tsuji, M. Koshiba, T. Shiraishi, “Finite element beam propagation method for three-dimensional optical waveguide structures,” J. Lightwave Technol. 15, 1728–1734 (1991).
    [CrossRef]
  4. E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
    [CrossRef]
  5. D. Schulz, C. Glingener, M. Bludszuweit, E. Voges, “Mixed finite element beam propagation method,” J. Lightwave Technol. 16, 1336–1342 (1998).
    [CrossRef]
  6. Y. Tsuji, M. Koshiba, “Finite element beam propagation method with perfectly matched layer boundary conditions for three-dimensional optical waveguides,” presented at the 4th International Workshop on Finite Elements for Microwave Engineering, Poitiers, France, Section F, July 10–11, 1998.
  7. A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
    [CrossRef]
  8. O. Mitomi, K. Kasaya, “An improved semivectorial beam propagation method using a finite-element scheme,” IEEE Photon. Technol. Lett. 10, 1754–1756 (1998).
    [CrossRef]
  9. A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
    [CrossRef]
  10. T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
    [CrossRef]
  11. S. V. Polstyanko, J. F. Lee, “H1 (curl) tangential vector finite element method for modeling anisotropic optical fibers,” J. Lightwave Technol. 13, 2290–2295 (1995).
    [CrossRef]
  12. O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
    [CrossRef]
  13. A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.
  14. P. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–224 (1994).
    [CrossRef]
  15. S. Selleri, M. Zoboli, “Performance comparison of finite element approaches for electromagnetic waveguides,” J. Opt. Soc. Am. A 14, 1460–1466 (1997).
    [CrossRef]
  16. B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).
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    [CrossRef]
  19. E. E. Kriezis, A. G. Papagiannakis, “A joint finite-difference and FFT full vectorial beam propagation scheme,” J. Lightwave Technol. 13, 692–700 (1995).
    [CrossRef]
  20. J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
    [CrossRef]
  21. V. P. Tzolov, M. Fontaine, “A passive polarization converter free of longitudinally periodic structure,” Opt. Commun. 127, 7–13 (1996).
    [CrossRef]
  22. J. Z. Huang, G. Nagy, R. Scamozzino, R. M. Osgood, “First realization of an ultracompact and single-mode integrated optical passive polarization converter,” presented at the 9th European Conference on Integrated Optics (ECIO’99)Torino, Italy, April 13–16, 1999.
  23. H. E. Hernandez-Figueroa, “Simple nonparaxial beam-propagation method for integrated optics,” J. Lightwave Technol. 12, 644–649 (1994).
    [CrossRef]
  24. S. Selleri, L. Vincetti, A. Cucinotta, “Finite element method resolution of nonlinear Helmholtz equation,” Opt. Quantum Electron. 30, 457–465 (1998).
    [CrossRef]

1999 (3)

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
[CrossRef]

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

1998 (4)

O. Mitomi, K. Kasaya, “An improved semivectorial beam propagation method using a finite-element scheme,” IEEE Photon. Technol. Lett. 10, 1754–1756 (1998).
[CrossRef]

E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
[CrossRef]

D. Schulz, C. Glingener, M. Bludszuweit, E. Voges, “Mixed finite element beam propagation method,” J. Lightwave Technol. 16, 1336–1342 (1998).
[CrossRef]

S. Selleri, L. Vincetti, A. Cucinotta, “Finite element method resolution of nonlinear Helmholtz equation,” Opt. Quantum Electron. 30, 457–465 (1998).
[CrossRef]

1997 (2)

H. E. Hernandez-Figueroa, “Efficient 3-D split operator finite element algorithm for scalar integrated optics,” IEEE Photon. Technol. Lett. 9, 351–353 (1997).
[CrossRef]

S. Selleri, M. Zoboli, “Performance comparison of finite element approaches for electromagnetic waveguides,” J. Opt. Soc. Am. A 14, 1460–1466 (1997).
[CrossRef]

1996 (1)

V. P. Tzolov, M. Fontaine, “A passive polarization converter free of longitudinally periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

1995 (3)

E. E. Kriezis, A. G. Papagiannakis, “A joint finite-difference and FFT full vectorial beam propagation scheme,” J. Lightwave Technol. 13, 692–700 (1995).
[CrossRef]

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

S. V. Polstyanko, J. F. Lee, “H1 (curl) tangential vector finite element method for modeling anisotropic optical fibers,” J. Lightwave Technol. 13, 2290–2295 (1995).
[CrossRef]

1994 (3)

P. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–224 (1994).
[CrossRef]

B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).

H. E. Hernandez-Figueroa, “Simple nonparaxial beam-propagation method for integrated optics,” J. Lightwave Technol. 12, 644–649 (1994).
[CrossRef]

1993 (1)

P. L. Liu, B. J. Li, “Semivectorial beam propagation by Lanczos reduction,” IEEE J. Quantum Electron. 29, 2385–2389 (1993).
[CrossRef]

1991 (2)

Y. Tsuji, M. Koshiba, T. Shiraishi, “Finite element beam propagation method for three-dimensional optical waveguide structures,” J. Lightwave Technol. 15, 1728–1734 (1991).
[CrossRef]

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

1981 (1)

Bahlmann, N.

Bludszuweit, M.

Cucinotta, A.

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
[CrossRef]

S. Selleri, L. Vincetti, A. Cucinotta, “Finite element method resolution of nonlinear Helmholtz equation,” Opt. Quantum Electron. 30, 457–465 (1998).
[CrossRef]

A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.

Davies, J. B.

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

Dillon, B. M.

B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).

Dotsch, H.

Fernandez, F. A.

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

Fontaine, M.

V. P. Tzolov, M. Fontaine, “A passive polarization converter free of longitudinally periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

Glingener, C.

Groen, F. H.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Hakimzadeh, F.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Hernandez-Figueroa, H. E.

H. E. Hernandez-Figueroa, “Efficient 3-D split operator finite element algorithm for scalar integrated optics,” IEEE Photon. Technol. Lett. 9, 351–353 (1997).
[CrossRef]

H. E. Hernandez-Figueroa, “Simple nonparaxial beam-propagation method for integrated optics,” J. Lightwave Technol. 12, 644–649 (1994).
[CrossRef]

Hertel, P.

Huang, J. Z.

J. Z. Huang, G. Nagy, R. Scamozzino, R. M. Osgood, “First realization of an ultracompact and single-mode integrated optical passive polarization converter,” presented at the 9th European Conference on Integrated Optics (ECIO’99)Torino, Italy, April 13–16, 1999.

Kasaya, K.

O. Mitomi, K. Kasaya, “An improved semivectorial beam propagation method using a finite-element scheme,” IEEE Photon. Technol. Lett. 10, 1754–1756 (1998).
[CrossRef]

Koch, T. B.

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

Koshiba, M.

Y. Tsuji, M. Koshiba, T. Shiraishi, “Finite element beam propagation method for three-dimensional optical waveguide structures,” J. Lightwave Technol. 15, 1728–1734 (1991).
[CrossRef]

Y. Tsuji, M. Koshiba, “Finite element beam propagation method with perfectly matched layer boundary conditions for three-dimensional optical waveguides,” presented at the 4th International Workshop on Finite Elements for Microwave Engineering, Poitiers, France, Section F, July 10–11, 1998.

Kriezis, E. E.

E. E. Kriezis, A. G. Papagiannakis, “A joint finite-difference and FFT full vectorial beam propagation scheme,” J. Lightwave Technol. 13, 692–700 (1995).
[CrossRef]

Lagasse, P.

Lee, J. F.

S. V. Polstyanko, J. F. Lee, “H1 (curl) tangential vector finite element method for modeling anisotropic optical fibers,” J. Lightwave Technol. 13, 2290–2295 (1995).
[CrossRef]

Lee, P. C.

P. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–224 (1994).
[CrossRef]

Li, B. J.

P. L. Liu, B. J. Li, “Semivectorial beam propagation by Lanczos reduction,” IEEE J. Quantum Electron. 29, 2385–2389 (1993).
[CrossRef]

Liu, P. L.

P. L. Liu, B. J. Li, “Semivectorial beam propagation by Lanczos reduction,” IEEE J. Quantum Electron. 29, 2385–2389 (1993).
[CrossRef]

Liu, P. T. S.

B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).

Lohmeyer, M.

Maerz, R.

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

Metaal, E. G.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Mitomi, O.

O. Mitomi, K. Kasaya, “An improved semivectorial beam propagation method using a finite-element scheme,” IEEE Photon. Technol. Lett. 10, 1754–1756 (1998).
[CrossRef]

Moerman, I.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Montanari, E.

E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
[CrossRef]

A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.

Nagy, G.

J. Z. Huang, G. Nagy, R. Scamozzino, R. M. Osgood, “First realization of an ultracompact and single-mode integrated optical passive polarization converter,” presented at the 9th European Conference on Integrated Optics (ECIO’99)Torino, Italy, April 13–16, 1999.

Oei, Y. S.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Osgood, R. M.

J. Z. Huang, G. Nagy, R. Scamozzino, R. M. Osgood, “First realization of an ultracompact and single-mode integrated optical passive polarization converter,” presented at the 9th European Conference on Integrated Optics (ECIO’99)Torino, Italy, April 13–16, 1999.

Papagiannakis, A. G.

E. E. Kriezis, A. G. Papagiannakis, “A joint finite-difference and FFT full vectorial beam propagation scheme,” J. Lightwave Technol. 13, 692–700 (1995).
[CrossRef]

Pedersen, J. W.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Pelosi, G.

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

Polstyanko, S. V.

S. V. Polstyanko, J. F. Lee, “H1 (curl) tangential vector finite element method for modeling anisotropic optical fibers,” J. Lightwave Technol. 13, 2290–2295 (1995).
[CrossRef]

Popkov, A. F.

Scamozzino, R.

J. Z. Huang, G. Nagy, R. Scamozzino, R. M. Osgood, “First realization of an ultracompact and single-mode integrated optical passive polarization converter,” presented at the 9th European Conference on Integrated Optics (ECIO’99)Torino, Italy, April 13–16, 1999.

Schulz, D.

Selleri, S.

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
[CrossRef]

E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
[CrossRef]

S. Selleri, L. Vincetti, A. Cucinotta, “Finite element method resolution of nonlinear Helmholtz equation,” Opt. Quantum Electron. 30, 457–465 (1998).
[CrossRef]

S. Selleri, M. Zoboli, “Performance comparison of finite element approaches for electromagnetic waveguides,” J. Opt. Soc. Am. A 14, 1460–1466 (1997).
[CrossRef]

A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.

Shiraishi, T.

Y. Tsuji, M. Koshiba, T. Shiraishi, “Finite element beam propagation method for three-dimensional optical waveguide structures,” J. Lightwave Technol. 15, 1728–1734 (1991).
[CrossRef]

Tsuji, Y.

Y. Tsuji, M. Koshiba, T. Shiraishi, “Finite element beam propagation method for three-dimensional optical waveguide structures,” J. Lightwave Technol. 15, 1728–1734 (1991).
[CrossRef]

Y. Tsuji, M. Koshiba, “Finite element beam propagation method with perfectly matched layer boundary conditions for three-dimensional optical waveguides,” presented at the 4th International Workshop on Finite Elements for Microwave Engineering, Poitiers, France, Section F, July 10–11, 1998.

Tzolov, V. P.

V. P. Tzolov, M. Fontaine, “A passive polarization converter free of longitudinally periodic structure,” Opt. Commun. 127, 7–13 (1996).
[CrossRef]

Van der Donk, J.

Van der Tol, J. J. G. M.

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

Van Roey, J.

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
[CrossRef]

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
[CrossRef]

S. Selleri, L. Vincetti, A. Cucinotta, “Finite element method resolution of nonlinear Helmholtz equation,” Opt. Quantum Electron. 30, 457–465 (1998).
[CrossRef]

A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.

Voges, E.

D. Schulz, C. Glingener, M. Bludszuweit, E. Voges, “Mixed finite element beam propagation method,” J. Lightwave Technol. 16, 1336–1342 (1998).
[CrossRef]

P. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–224 (1994).
[CrossRef]

Webb, J. P.

B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).

Zhuromskyy, O.

Zoboli, M.

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti, M. Zoboli, “Perfectly matched anisotropic layers for optical waveguides analysis through the finite element beam propagation method,” Microwave Opt. Technol. Lett. 23, 67–69 (1999).
[CrossRef]

E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides,” J. Lightwave Technol. 16, 703–714 (1998).
[CrossRef]

S. Selleri, M. Zoboli, “Performance comparison of finite element approaches for electromagnetic waveguides,” J. Opt. Soc. Am. A 14, 1460–1466 (1997).
[CrossRef]

A. Cucinotta, E. Montanari, S. Selleri, L. Vincetti, M. Zoboli, “Finite-element full-vectorial propagation analysis for three dimensional anisotropic waveguides,” presented at the International Conference on Electromagnetics in Advanced Applications (ICEAA 97), Torino, Italy, September 15–18, 1997.

IEEE J. Quantum Electron. (1)

P. L. Liu, B. J. Li, “Semivectorial beam propagation by Lanczos reduction,” IEEE J. Quantum Electron. 29, 2385–2389 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

H. E. Hernandez-Figueroa, “Efficient 3-D split operator finite element algorithm for scalar integrated optics,” IEEE Photon. Technol. Lett. 9, 351–353 (1997).
[CrossRef]

O. Mitomi, K. Kasaya, “An improved semivectorial beam propagation method using a finite-element scheme,” IEEE Photon. Technol. Lett. 10, 1754–1756 (1998).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, “Nonlinear finite-element semivectorial propagation method for three dimensional optical waveguides,” IEEE Photon. Technol. Lett. 11, 209–211 (1999).
[CrossRef]

J. J. G. M. Van der Tol, J. W. Pedersen, E. G. Metaal, F. Hakimzadeh, Y. S. Oei, F. H. Groen, I. Moerman, “Realization of a short integrated optic passive polarization converter,” IEEE Photon. Technol. Lett. 7, 893–895 (1995).
[CrossRef]

IEEE Trans. Magn. (1)

T. B. Koch, J. B. Davies, F. A. Fernandez, R. Maerz, “Computation of wave propagation in integrated optical devices using z-transient variational principles,” IEEE Trans. Magn. 27, 3876–3879 (1991).
[CrossRef]

Int. J. Computation Math. Electr. Electron. Eng. (1)

B. M. Dillon, P. T. S. Liu, J. P. Webb, “Spurious modes in quadrilateral and triangular edge elements,” Int. J. Computation Math. Electr. Electron. Eng. 13, Suppl. A, 311–316 (1994).

J. Lightwave Technol. (8)

E. E. Kriezis, A. G. Papagiannakis, “A joint finite-difference and FFT full vectorial beam propagation scheme,” J. Lightwave Technol. 13, 692–700 (1995).
[CrossRef]

P. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–224 (1994).
[CrossRef]

S. V. Polstyanko, J. F. Lee, “H1 (curl) tangential vector finite element method for modeling anisotropic optical fibers,” J. Lightwave Technol. 13, 2290–2295 (1995).
[CrossRef]

O. Zhuromskyy, M. Lohmeyer, N. Bahlmann, H. Dotsch, P. Hertel, A. F. Popkov, “Analysis of polarization independent Mach–Zehnder-type integrated optical isolator,” J. Lightwave Technol. 17, 1200–1205 (1999).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Hx shape error for the fundamental Hx polarized mode versus the core refractive index. The cladding refractive index is ncl=1.5 and the core radius rco=1 μm. A normalized frequency ν=2.25 is assumed. Two vectorial, semivectorial, and scalar formulations are considered.

Fig. 2
Fig. 2

Hy shape error. Other parameters as in Fig. 1.

Fig. 3
Fig. 3

Hz shape error. Other parameters as in Fig. 1.

Fig. 4
Fig. 4

Effective index error e=(neff-na)/na, where neff is the computed effective index and na the analytical value. Other parameters as in Fig. 1.

Fig. 5
Fig. 5

Computational time of the two vectorial formulations versus the number of unknowns.

Fig. 6
Fig. 6

(a) Rib waveguide parameters: W=2 μm, H=1.1 μm, S=0.2 μm, na=1, nc=3.44, and ns=3.34. (b) Polarization converter parameters: W=2 μm, W1=1 μm, H=0.8 μm, H1=0.2 μm, S=0.2 μm, na=1, nc=3.4, and ns=3.27.

Fig. 7
Fig. 7

Polarization converter mesh, with 1318 triangles.

Fig. 8
Fig. 8

Hx (left), Hy (center), and Hz (right) distributions for propagation distances of z=0, 62.5, 125, 250, and 500 μm.

Tables (2)

Tables Icon

Table 1 Comparison of the Effective Index Obtained with Different BPM Formulations, Nodal and Edge-Based Mode Solvers, and Other Data Reported in the Literature

Tables Icon

Table 2 Comparison of the Polarization Conversion Length L Obtained with Different BPM Formulations, Nodal and Edge-Based Mode Solvers, and Other Data Reported in the Literature

Equations (12)

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

¯¯r=x000y000z,μ¯¯r=μx000μy000μz.
¯×(p¯¯¯×Φ¯)-k02q¯¯Φ¯=0;
-p¯¯* 2ϕ¯tz2+2jβp¯¯* ϕ¯tz=-¯t[pz(¯t×ϕ¯t)zˆ]×zˆ+(k02q¯¯t-p¯¯*β2)ϕ¯t-p¯¯* z (¯tϕz)+jβp¯¯*¯tϕz,
p¯¯*=py00px,q¯¯t=qx00qy.
qz ϕzz=jβqzϕz-¯t(q¯¯tϕ¯t),
¯t×[(p¯¯*¯tϕz)×zˆ]-¯t×p¯¯*z-jβϕ¯t×zˆ
-k02qzzˆ=0,
2jβps ϕhz=(qhk02-psβ2)ϕh+s pz ϕhs+ps h jβϕz-ϕzz,
qz ϕzz=jβqzϕz-qhϕhh,
2jβpy ϕxz=(qxk02-pyβ2)ϕx+x pyqxqz ϕxx+y p ϕxy,
ϕϕ-ϕaϕa,
L=λ2(neff 1-neff 2),

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