Abstract

The coordinate transformation method (C method) with adaptive spatial resolution and the Fourier modal method (FMM) are compared in the case of conducting discontinuous multilevel gratings in TM polarization. A procedure permitting analysis of such gratings more efficiently with the C method than with the FMM is presented. The C method is observed to converge more rapidly than the FMM, whose instabilities are shown to harm the convergence in the aforementioned case.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  9. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. 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]
  15. J. Turunen, “Form-birefringence limits of Fourier-expansion methods in grating theory,” J. Opt. Soc. Am. A 13, 1013–1018 (1996).
    [CrossRef]
  16. G. Granet, B. Guizal, “Efficient implementation for the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]

2002 (2)

2001 (1)

1999 (2)

1996 (6)

1995 (2)

1994 (1)

1986 (1)

E. Popov, L. Mashev, “Convergence of Rayleigh–Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593–605 (1986).
[CrossRef]

1982 (2)

1980 (1)

J. Chandezon, D. Maystre, G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).
[CrossRef]

1978 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

Chandezon, J.

Cornet, G.

Cotter, N. P. K.

Dupuis, M. T.

Gaylord, T. K.

Gralak, B.

Granet, G.

Grann, E. B.

Guizal, B.

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (MacMillan, New York, 1968).

Honkanen, M.

Knop, K.

Lalanne, P.

Li, L.

Mashev, L.

E. Popov, L. Mashev, “Convergence of Rayleigh–Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593–605 (1986).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, Electricity and Magnetism (Dover, New York, 1954), Vol. II.

Maystre, D.

J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839–846 (1982).
[CrossRef]

J. Chandezon, D. Maystre, G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Nevière, M.

Petit, R.

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 1, pp. 1–40.

Plumey, J. P.

Plumey, J.-P.

Pommet, D. A.

Popov, E.

E. Popov, M. Nevière, B. Gralak, G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19, 33–42 (2002).
[CrossRef]

E. Popov, L. Mashev, “Convergence of Rayleigh–Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593–605 (1986).
[CrossRef]

Preist, T. W.

Raniriharinosy, K.

Raoult, G.

J. Chandezon, D. Maystre, G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).
[CrossRef]

Sambles, J. R.

Tayeb, G.

Turunen, J.

J. Turunen, “Form-birefringence limits of Fourier-expansion methods in grating theory,” J. Opt. Soc. Am. A 13, 1013–1018 (1996).
[CrossRef]

J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, Cornwall, UK, 1997), Chap. 2, pp. 31–52.

Vallius, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

Appl. Opt. (1)

J. Opt. (Paris) (1)

J. Chandezon, D. Maystre, G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (12)

G. Granet, J. Chandezon, J. P. Plumey, K. Raniriharinosy, “Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings,” J. Opt. Soc. Am. A 18, 2102–2108 (2001).
[CrossRef]

E. Popov, M. Nevière, B. Gralak, G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19, 33–42 (2002).
[CrossRef]

J. P. Plumey, G. Granet, “Generalization of the coordinate transformation method with application to surface-relief gratings,” J. Opt. Soc. Am. A 16, 508–516 (1999).
[CrossRef]

L. Li, “Multilayer coated gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994).
[CrossRef]

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]

J. Turunen, “Form-birefringence limits of Fourier-expansion methods in grating theory,” J. Opt. Soc. Am. A 13, 1013–1018 (1996).
[CrossRef]

G. Granet, B. Guizal, “Efficient implementation for the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
[CrossRef]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
[CrossRef]

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
[CrossRef]

L. Li, J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
[CrossRef]

M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
[CrossRef]

N. P. K. Cotter, T. W. Preist, J. R. Sambles, “Scattering matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
[CrossRef]

Opt. Acta (1)

E. Popov, L. Mashev, “Convergence of Rayleigh–Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593–605 (1986).
[CrossRef]

Opt. Express (1)

Other (5)

J. Turunen, “Diffraction theory of microrelief gratings,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, Cornwall, UK, 1997), Chap. 2, pp. 31–52.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999).

J. C. Maxwell, Electricity and Magnetism (Dover, New York, 1954), Vol. II.

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 1, pp. 1–40.

R. F. Harrington, Field Computation by Moment Methods (MacMillan, New York, 1968).

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