Abstract

Recently, we described a simple but efficient 2-D bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices. Complex coordinate transformation was used as an efficient absorbing boundary condition. In this paper, we systematically extend this algorithm to 3-D structures.

© 2012 IEEE

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  1. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2004).
  2. S. Obayya, Computational Photonics (Wiley, 2010).
  3. P. Bienstman, Rigorous and efficient modelling of wavelength scale photonic components Ph.D. dissertation Univ. GentGentBelgium (2001).
  4. G. Sztefka, H.-P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554-557 (1993).
  5. A. Sudbø, P. I. Jensen, "Stable bidirectional eigenmode propagation of optical fields in waveguide devices," Integr. Photon. Res. MontereyCA (1995) Paper IThB4-1-4/27-29.
  6. E. Silberstein, P. Lalanne, J. P. Hugonin, Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Amer. A 18, 2865-2875 (2001).
  7. J. P. Hugonin, P. Lalanne, I. d. Villar, I. R. Matias, "Fourier modal methods for modelling optical dielectric waveguides," Opt. Quantum Electron. 37, 107-119 (2005).
  8. J. ?tyroký, I. Richter, P. Kwiecien, "Critical comparison of three modal methods: Bidirectional eigenmode expansion propagation method, aperiodic rigorous coupled mode analysis, and harmonic expansion method," Proc. Photon. North (2008) pp. K991.
  9. W. C. Chew, J. M. Jin, E. Michielsen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Technol. Lett. 15, 383-369 (1997).
  10. J. P. Hugonin, P. Lalanne, "Perfectly matched layers as nonlinear coordinate transforms: A generalized formalization," J. Opt. Soc. Amer. A 22, 1844-1849 (2005).
  11. P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A 13, 779-784 (1996).
  12. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Amer. A 13, 1870-1876 (1996).
  13. L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt. 5, 345-355 (2003).
  14. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Amer. A 24, 2880-2890 (2007).
  15. R. Antos, "Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures," Opt. Exp. 17, 7269-7274 (2009).
  16. R. Antos, "Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals," Opt. Exp. 18, 27511-27524 (2010).
  17. S. Essig, K. Busch, "Generation of adaptive coordinates and their use in the Fourier Modal Method," Opt. Exp. 18, 23258-23274 (2010).
  18. J. ?tyroký, "A simple bi-directional mode expansion propagation algorithm based on modes of a parallel-plate waveguide," Opt. Quantum Electron. 38, 45-62 (2006).
  19. J. ?tyroký, "Improved bidirectional-mode expansion propagation algorithm based on Fourier series," J. Lightw. Technol. 25, 2321-2330 (2007).
  20. J. ?tyroký, "Efficient boundary conditions for bidirectional propagation algorithm based on Fourier series," J. Lightw. Technol. 27, 2575-2582 (2009).
  21. G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Amer. A 16, 2510-2516 (1999).
  22. T. Vallius, M. Honkanen, "Reformulation of the Fourier modal method with adaptive spatial resolution: Application to multilevel profiles," Opt. Exp. 10, 24-34 (2002).
  23. P. Debackere, P. Bienstman, R. Baets, "Adaptive spatial resolution: Application to surface plasmon waveguide modes," Opt. Quantum Electron. 38, 857-867 (2006).
  24. J. ?tyroký, P. Kwiecien, I. Richter, "Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution," J. Lightw. Technol. 28, 2969-2976 (2010).
  25. A. S. Sudbø, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," Pure Appl. Opt. 3, 381-388 (1994).
  26. R. F. Oulton, G. Bartal, D. F. P. Pile, X. Zhang, "Confinement and propagation characteristics of subwavelength plasmonic modes," New J. Phys. 10, 105018 (2008).
  27. H.-S. Chu, Y. A. Akimov, P. Bai, E.-P. Li, "Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale," J. Opt. Soc. Amer. B 28, 2895-2901 (2011).
  28. L. Prkna, M. Hubalek, J. ?tyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Topics Quantum Electron. 11, 217-223 (2005).
  29. P. Lalanne, E. Silberstein, "Fourier-modal methods applied to waveguide computational problems," Opt. Lett. 25, 1092-1094 (2000).
  30. A. B. Fallahkhair, K. S. Li, T. E. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).
  31. J. ?tyroký, P. Kwiecien, I. Richter, "Fourier series based 3D Bi-directional propagation algorithm for integrated photonics," presented at the 18th Eur. Conf. Integrated Optics Sitges-BarcelonaSpain (2012).

2011

H.-S. Chu, Y. A. Akimov, P. Bai, E.-P. Li, "Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale," J. Opt. Soc. Amer. B 28, 2895-2901 (2011).

2010

J. ?tyroký, P. Kwiecien, I. Richter, "Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution," J. Lightw. Technol. 28, 2969-2976 (2010).

R. Antos, "Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals," Opt. Exp. 18, 27511-27524 (2010).

S. Essig, K. Busch, "Generation of adaptive coordinates and their use in the Fourier Modal Method," Opt. Exp. 18, 23258-23274 (2010).

2009

R. Antos, "Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures," Opt. Exp. 17, 7269-7274 (2009).

J. ?tyroký, "Efficient boundary conditions for bidirectional propagation algorithm based on Fourier series," J. Lightw. Technol. 27, 2575-2582 (2009).

2008

R. F. Oulton, G. Bartal, D. F. P. Pile, X. Zhang, "Confinement and propagation characteristics of subwavelength plasmonic modes," New J. Phys. 10, 105018 (2008).

A. B. Fallahkhair, K. S. Li, T. E. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).

2007

J. ?tyroký, "Improved bidirectional-mode expansion propagation algorithm based on Fourier series," J. Lightw. Technol. 25, 2321-2330 (2007).

T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Amer. A 24, 2880-2890 (2007).

2006

J. ?tyroký, "A simple bi-directional mode expansion propagation algorithm based on modes of a parallel-plate waveguide," Opt. Quantum Electron. 38, 45-62 (2006).

P. Debackere, P. Bienstman, R. Baets, "Adaptive spatial resolution: Application to surface plasmon waveguide modes," Opt. Quantum Electron. 38, 857-867 (2006).

2005

J. P. Hugonin, P. Lalanne, "Perfectly matched layers as nonlinear coordinate transforms: A generalized formalization," J. Opt. Soc. Amer. A 22, 1844-1849 (2005).

J. P. Hugonin, P. Lalanne, I. d. Villar, I. R. Matias, "Fourier modal methods for modelling optical dielectric waveguides," Opt. Quantum Electron. 37, 107-119 (2005).

L. Prkna, M. Hubalek, J. ?tyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Topics Quantum Electron. 11, 217-223 (2005).

2003

L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt. 5, 345-355 (2003).

2002

T. Vallius, M. Honkanen, "Reformulation of the Fourier modal method with adaptive spatial resolution: Application to multilevel profiles," Opt. Exp. 10, 24-34 (2002).

2001

E. Silberstein, P. Lalanne, J. P. Hugonin, Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Amer. A 18, 2865-2875 (2001).

2000

1999

G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Amer. A 16, 2510-2516 (1999).

1997

W. C. Chew, J. M. Jin, E. Michielsen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Technol. Lett. 15, 383-369 (1997).

1996

P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A 13, 779-784 (1996).

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Amer. A 13, 1870-1876 (1996).

1994

A. S. Sudbø, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," Pure Appl. Opt. 3, 381-388 (1994).

1993

G. Sztefka, H.-P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554-557 (1993).

IEEE J. Sel. Topics Quantum Electron.

L. Prkna, M. Hubalek, J. ?tyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Topics Quantum Electron. 11, 217-223 (2005).

IEEE Photon. Technol. Lett.

G. Sztefka, H.-P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554-557 (1993).

J. Opt. Soc. Amer. A

P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A 13, 779-784 (1996).

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Amer. A 13, 1870-1876 (1996).

J. Lightw. Technol.

A. B. Fallahkhair, K. S. Li, T. E. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).

J. Lightw. Technol.

J. ?tyroký, "Improved bidirectional-mode expansion propagation algorithm based on Fourier series," J. Lightw. Technol. 25, 2321-2330 (2007).

J. ?tyroký, "Efficient boundary conditions for bidirectional propagation algorithm based on Fourier series," J. Lightw. Technol. 27, 2575-2582 (2009).

J. ?tyroký, P. Kwiecien, I. Richter, "Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution," J. Lightw. Technol. 28, 2969-2976 (2010).

J. Opt. A: Pure Appl. Opt.

L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A: Pure Appl. Opt. 5, 345-355 (2003).

J. Opt. Soc. Amer. A

T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Amer. A 24, 2880-2890 (2007).

J. Opt. Soc. Amer. A

E. Silberstein, P. Lalanne, J. P. Hugonin, Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Amer. A 18, 2865-2875 (2001).

J. P. Hugonin, P. Lalanne, "Perfectly matched layers as nonlinear coordinate transforms: A generalized formalization," J. Opt. Soc. Amer. A 22, 1844-1849 (2005).

G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Amer. A 16, 2510-2516 (1999).

J. Opt. Soc. Amer. B

H.-S. Chu, Y. A. Akimov, P. Bai, E.-P. Li, "Hybrid dielectric-loaded plasmonic waveguide and wavelength selective components for efficiently controlling light at subwavelength scale," J. Opt. Soc. Amer. B 28, 2895-2901 (2011).

Microw. Opt. Technol. Lett.

W. C. Chew, J. M. Jin, E. Michielsen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Technol. Lett. 15, 383-369 (1997).

New J. Phys.

R. F. Oulton, G. Bartal, D. F. P. Pile, X. Zhang, "Confinement and propagation characteristics of subwavelength plasmonic modes," New J. Phys. 10, 105018 (2008).

Opt. Exp.

T. Vallius, M. Honkanen, "Reformulation of the Fourier modal method with adaptive spatial resolution: Application to multilevel profiles," Opt. Exp. 10, 24-34 (2002).

R. Antos, "Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures," Opt. Exp. 17, 7269-7274 (2009).

R. Antos, "Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals," Opt. Exp. 18, 27511-27524 (2010).

S. Essig, K. Busch, "Generation of adaptive coordinates and their use in the Fourier Modal Method," Opt. Exp. 18, 23258-23274 (2010).

Opt. Lett.

Opt. Quantum Electron.

P. Debackere, P. Bienstman, R. Baets, "Adaptive spatial resolution: Application to surface plasmon waveguide modes," Opt. Quantum Electron. 38, 857-867 (2006).

J. P. Hugonin, P. Lalanne, I. d. Villar, I. R. Matias, "Fourier modal methods for modelling optical dielectric waveguides," Opt. Quantum Electron. 37, 107-119 (2005).

Opt. Quantum Electron.

J. ?tyroký, "A simple bi-directional mode expansion propagation algorithm based on modes of a parallel-plate waveguide," Opt. Quantum Electron. 38, 45-62 (2006).

Pure Appl. Opt.

A. S. Sudbø, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," Pure Appl. Opt. 3, 381-388 (1994).

Other

J. ?tyroký, P. Kwiecien, I. Richter, "Fourier series based 3D Bi-directional propagation algorithm for integrated photonics," presented at the 18th Eur. Conf. Integrated Optics Sitges-BarcelonaSpain (2012).

J. ?tyroký, I. Richter, P. Kwiecien, "Critical comparison of three modal methods: Bidirectional eigenmode expansion propagation method, aperiodic rigorous coupled mode analysis, and harmonic expansion method," Proc. Photon. North (2008) pp. K991.

A. Sudbø, P. I. Jensen, "Stable bidirectional eigenmode propagation of optical fields in waveguide devices," Integr. Photon. Res. MontereyCA (1995) Paper IThB4-1-4/27-29.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2004).

S. Obayya, Computational Photonics (Wiley, 2010).

P. Bienstman, Rigorous and efficient modelling of wavelength scale photonic components Ph.D. dissertation Univ. GentGentBelgium (2001).

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