Abstract

Recently we described the implementation of complex coordinate transformation as boundary conditions into a bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices. In this communication we report on the implementation of an additional coordinate transformation known as adaptive spatial resolution into this algorithm. It helps significantly reduce the number of expansion terms needed to reach required accuracy especially for photonics structures containing layers of very different thicknesses and/or optical properties, e.g., metal layers.

© 2010 IEEE

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  2. G. Sztefka, H.-P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554-557 (1993).
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  6. P. Lalanne, E. Silberstein, "Fourier-modal methods applied to waveguide computational problems," Opt. Lett. 25, 1092-1094 (2000).
  7. "Use of grating theories in integrated optics," J. Opt. Soc. Amer. A 18, 2865-2875 (2001).
  8. 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).
  9. C. Sauvan, P. Lalanna, J. P. Hugonin, "Truncation rules for modelling with Galerkin method in electromagnetic theory," Opt. Quantum Electron. 36, 271-284 (2004).
  10. J. Čtyroký, "A simple bidirectional mode expansion propagation algorithm based on modes of a parallel-plate waveguide," Opt. Quantum Electron. 38, 45-62 (2006).
  11. J. Čtyroký, "Improved bidirectional-mode expansion propagation algorithm based on Fourier series," J. Lightw. Technol. 25, 2321-2330 (2007).
  12. J. P. Hugonin, P. Lalanne, "Perfectly matched layers as nonlinear coordinate transforms: A generalized formalization," J. Opt. Soc. Amer. A 22, 1844-1849 (2005).
  13. G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Amer. A 16, 2510-2516 (1999).
  14. T. Vallius, M. Honkanen, "Reformulation of the Fourier modal method with adaptive spatial resolution: Application to multilevel profiles," Opt. Exp. 10, 24-34 (2002).
  15. P. Debackere, P. Bienstman, R. Baets, "Adaptive spatial resolution: Application to surface plasmon waveguide modes," Opt. Quantum Electron. 38, 857-867 (2006).
  16. J. Čtyroký, "Efficient boundary conditions for bidirectional propagation algorithm based on Fourier series," J. Lightw. Technol. 27, 2575-2582 (2009).
  17. M. Sumetsky, "Whispering-gallery-bottle microcavities: The three-dimensional etalon," Opt. Lett. 29, 8-10 (2004).
  18. B. Guizal, H. Yala, D. Felbacq, "Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution," Opt. Lett. 34, 2790-2792 (2009).
  19. C. E. Rüter, K. G. Makris, R. E-Ganainy, D. N. Christouildes, M. Segev, D. Kip, "Observation of parity-time symmetry in optics," Nature Phys. 6, 192-195 (2010).

2010

C. E. Rüter, K. G. Makris, R. E-Ganainy, D. N. Christouildes, M. Segev, D. Kip, "Observation of parity-time symmetry in optics," Nature Phys. 6, 192-195 (2010).

2009

B. Guizal, H. Yala, D. Felbacq, "Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution," Opt. Lett. 34, 2790-2792 (2009).

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

2007

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

2006

J. Čtyroký, "A simple bidirectional 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).

2004

C. Sauvan, P. Lalanna, J. P. Hugonin, "Truncation rules for modelling with Galerkin method in electromagnetic theory," Opt. Quantum Electron. 36, 271-284 (2004).

M. Sumetsky, "Whispering-gallery-bottle microcavities: The three-dimensional etalon," Opt. Lett. 29, 8-10 (2004).

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

"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).

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).

1993

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

1984

J. Chilwell, I. Hodgkinson, "Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection prism-loaded waveguides," J. Opt. Soc. Amer. A-1, 742-753 (1984).

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. Lightw. Technol.

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

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

J. Opt. Soc. Amer.

J. Chilwell, I. Hodgkinson, "Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection prism-loaded waveguides," J. Opt. Soc. Amer. A-1, 742-753 (1984).

J. Opt. Soc. Amer. A

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).

"Use of grating theories in integrated optics," J. Opt. Soc. Amer. A 18, 2865-2875 (2001).

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).

Nature Phys.

C. E. Rüter, K. G. Makris, R. E-Ganainy, D. N. Christouildes, M. Segev, D. Kip, "Observation of parity-time symmetry in optics," Nature Phys. 6, 192-195 (2010).

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).

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).

C. Sauvan, P. Lalanna, J. P. Hugonin, "Truncation rules for modelling with Galerkin method in electromagnetic theory," Opt. Quantum Electron. 36, 271-284 (2004).

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

Other

P. Bienstman, Rigorous and Efficient Modelling of Wavelength Scale Photonic Components Ph.D. dissertation University of GentBelgium (2001).

P. Bienstman, http://camfr.sourceforge.net/ (2003).

H. Berends, DBR Grating Spectral Filters for Optical Waveguide Sensors Ph.D. dissertationTU TwenteEnschede (1997).

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