Abstract

The concepts of adaptive coordinates and adaptive spatial resolution have proved to be a valuable tool to improve the convergence characteristics of the Fourier Modal Method (FMM), especially for metallo-dielectric systems. Yet, only two-dimensional adaptive coordinates were used so far. This paper presents the first systematic construction of three-dimensional adaptive coordinate and adaptive spatial resolution transformations in the context of the FMM. For that, the construction of a three-dimensional mesh for a periodic system consisting of two layers of mutually rotated, metallic crosses is discussed. The main impact of this method is that it can be used with any classic FMM code that is able to solve the large FMM eigenproblem. Since the transformation starts and ends in a Cartesian mesh, only the transformed material tensors need to be computed and entered into an existing FMM code.

© 2014 Optical Society of America

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  1. K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
    [CrossRef]
  2. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1034 (1996).
    [CrossRef]
  3. P. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  4. G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
    [CrossRef]
  5. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  6. 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]
  7. G. Granet, J.-P. Plumey, “Parametric formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. A 4, S145–S149 (2002).
    [CrossRef]
  8. T. Vallius, M. Honkanen, “Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel profiles,” Opt. Express 10, 24–34 (2002).
    [CrossRef] [PubMed]
  9. T. Weiss, G. Granet, N. A. Gippius, S. G. Tikhodeev, H. Giessen, “Matched coordinates and adaptive spatial resolution in the Fourier modal method,” Opt. Express 17, 8051–8061 (2009).
    [CrossRef] [PubMed]
  10. S. Essig, K. Busch, “Generation of adaptive coordinates and their use in the Fourier Modal Method,” Opt. Express 18, 23258–23274 (2010).
    [CrossRef] [PubMed]
  11. J. Küchenmeister, T. Zebrowski, K. Busch, “A construction guide to analytically generated meshes for the Fourier Modal Method,” Opt. Express 20, 17319–17347 (2012).
    [CrossRef] [PubMed]
  12. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 2501–2503 (2009).
    [CrossRef] [PubMed]
  13. V. Liu, S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
    [CrossRef]
  14. H. Kim, J. Park, B. Lee, Fourier Modal Method and its Applications in Computational Nanophotonics (CRC Press, 2012).
  15. L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A 5, 345–355 (2003).
    [CrossRef]
  16. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
    [CrossRef]

2012 (2)

J. Küchenmeister, T. Zebrowski, K. Busch, “A construction guide to analytically generated meshes for the Fourier Modal Method,” Opt. Express 20, 17319–17347 (2012).
[CrossRef] [PubMed]

V. Liu, S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
[CrossRef]

2010 (1)

2009 (2)

2007 (1)

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

2005 (1)

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

2003 (1)

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A 5, 345–355 (2003).
[CrossRef]

2002 (2)

G. Granet, J.-P. Plumey, “Parametric formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. A 4, S145–S149 (2002).
[CrossRef]

T. Vallius, M. Honkanen, “Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel profiles,” Opt. Express 10, 24–34 (2002).
[CrossRef] [PubMed]

1999 (1)

1996 (4)

Barchiesi, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Busch, K.

Decker, M.

Essig, S.

Fan, S.

V. Liu, S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
[CrossRef]

Giessen, H.

Gippius, N. A.

Granet, G.

Grimault, A.-S.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Guizal, B.

Honkanen, M.

Kim, H.

H. Kim, J. Park, B. Lee, Fourier Modal Method and its Applications in Computational Nanophotonics (CRC Press, 2012).

Kriegler, C. E.

Küchenmeister, J.

Lalanne, P.

Lamy de la Chapelle, M.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Lee, B.

H. Kim, J. Park, B. Lee, Fourier Modal Method and its Applications in Computational Nanophotonics (CRC Press, 2012).

Li, L.

Linden, S.

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 2501–2503 (2009).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Liu, V.

V. Liu, S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
[CrossRef]

Macías, D.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Mingaleev, S. F.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Morris, G. M.

Park, J.

H. Kim, J. Park, B. Lee, Fourier Modal Method and its Applications in Computational Nanophotonics (CRC Press, 2012).

Plumey, J.-P.

G. Granet, J.-P. Plumey, “Parametric formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. A 4, S145–S149 (2002).
[CrossRef]

Ruther, M.

Soukoulis, C. M.

Tikhodeev, S. G.

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Vallius, T.

Vial, A.

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

von Freymann, G.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Wegener, M.

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 2501–2503 (2009).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Weiss, T.

Zebrowski, T.

Zhou, J.

Comput. Phys. Commun. (1)

V. Liu, S. Fan, “S4: A free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183, 2233–2244 (2012).
[CrossRef]

J. Opt. A (2)

L. Li, “Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors,” J. Opt. A 5, 345–355 (2003).
[CrossRef]

G. Granet, J.-P. Plumey, “Parametric formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. A 4, S145–S149 (2002).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Express (4)

Opt. Lett. (1)

Phys. Rep. (1)

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Phys. Rev. B (1)

A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, M. Lamy de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Other (1)

H. Kim, J. Park, B. Lee, Fourier Modal Method and its Applications in Computational Nanophotonics (CRC Press, 2012).

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