Abstract

Several improvements have been introduced for the Fourier modal method in the last fifteen years. Among those, the formulation of the correct factorization rules and adaptive spatial resolution have been crucial steps towards a fast converging scheme, but an application to arbitrary two-dimensional shapes is quite complicated.We present a generalization of the scheme for non-trivial planar geometries using a covariant formulation of Maxwell’s equations and a matched coordinate system aligned along the interfaces of the structure that can be easily combined with adaptive spatial resolution. In addition, a symmetric application of Fourier factorization is discussed.

© 2009 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
    [CrossRef]
  2. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B66,  45,102-1-17 (2002).
  3. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  4. G. Granet, "Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution," J. Opt. Soc. Am. A 16, 2510-2516 (1999).
    [CrossRef]
  5. G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A 4, 145-149 (2002).
  6. P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
    [CrossRef]
  7. E. Popov and M. Nevière, "Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A 18, 2886-2894 (2001).
    [CrossRef]
  8. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Am. A 24, 2880-2890 (2007).
    [CrossRef]
  9. P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).
  10. J. H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics (Trafford Publishing, 2001).
  11. E. J. Post, Formal structure of Electromagnetism (North Holland, Amsterdam, 1962).
  12. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  13. L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A 5, 345-355 (2003).
  14. J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley and Sons, 1999).

2008 (1)

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

2007 (1)

2003 (1)

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

2002 (1)

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A 4, 145-149 (2002).

2001 (1)

1999 (2)

D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

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

1997 (2)

1996 (1)

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

Frenner, K.

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

G¨otz, P.

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

Granet, G.

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A 4, 145-149 (2002).

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

Kerwien, N.

Lalanne, P.

Li, L.

Nevière, M.

Osten, W.

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

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

Plumey, J. P.

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A 4, 145-149 (2002).

Popov, E.

Rafler, S.

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

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

Ruoff, J.

Schuster, T.

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

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

Whittaker, D. M.

D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

J. Opt. A (2)

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A 4, 145-149 (2002).

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

J. Opt. Soc. Am. A (6)

Opt. Ex. (1)

P. G¨otz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Ex. 16, 17,295-17,301 (2008).

Phys. Rev. B (1)

D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999).
[CrossRef]

Other (4)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B66,  45,102-1-17 (2002).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley and Sons, 1999).

J. H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics (Trafford Publishing, 2001).

E. J. Post, Formal structure of Electromagnetism (North Holland, Amsterdam, 1962).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics