Matched coordinates and adaptive spatial resolution in the Fourier modal method

doi:10.1364/OE.17.008051

Matched coordinates and adaptive spatial resolution in the Fourier modal method

Thomas Weiss, Gérard Granet, Nikolay A. Gippius, Sergei G. Tikhodeev, and Harald Giessen »View Author Affiliations

Optics Express, Vol. 17, Issue 10, pp. 8051-8061 (2009)
http://dx.doi.org/10.1364/OE.17.008051

View Full Text Article

Enhanced HTML Acrobat PDF (154 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Abstract
Article Info
References (14)
Cited By
Figures (5)
Metrics
Related Content

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.

OCIS Codes
(090.1970) Holography : Diffractive optics
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 20, 2009
Revised Manuscript: April 10, 2009
Manuscript Accepted: April 21, 2009
Published: April 29, 2009

Citation
Thomas Weiss, Gérard Granet, Nikolay A. Gippius, Sergei G. Tikhodeev, and Harald Giessen, "Matched coordinates and adaptive spatial resolution in the Fourier modal method," Opt. Express 17, 8051-8061 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8051

Sort: Author | Year | Journal | Reset

References

D. M. Whittaker and I. S. Culshaw, "Scattering Matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]
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). [CrossRef]
L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [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]
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). [CrossRef]
P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997). [CrossRef]
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]
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]
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).
J. H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics (Trafford Publishing, 2001).
E. J. Post, Formal structure of Electromagnetism (North Holland, Amsterdam, 1962).
L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997). [CrossRef]
L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A 5, 345-355 (2003). [CrossRef]
J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley and Sons, 1999).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Click here to see a list of articles that cite this paper

Figures


Fig. 1. (a)	Fig. 2.	Fig. 3.


Fig. 4.	Fig. 5.

« Previous Article | Next Article »

OSA is a member of CrossRef.

[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). [CrossRef]

[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). [CrossRef]

[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). [CrossRef]

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

OpticsInfoBase

Optics Express

Matched coordinates and adaptive spatial resolution in the Fourier modal method