Abstract

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]
  2. 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]
  3. E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
    [CrossRef]
  4. S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
    [CrossRef]
  5. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994); Errata 13, 543 (1996).
  6. J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
    [CrossRef]
  7. G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
    [CrossRef]
  8. L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
    [CrossRef]
  9. T. W. Preist, N. P. K. Cotter, J. R. Sambles, “Periodic multilayer gratings of arbitrary shape,” J. Opt. Soc. Am. A 12, 1740–1748 (1995).
    [CrossRef]
  10. J.-P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
    [CrossRef]
  11. T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).
  12. G. Granet, “Analysis of diffraction by crossed gratings using a non-orthogonal coordinate system,” Pure Appl. Opt. 4, 777–793 (1995).
    [CrossRef]
  13. G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121–1131 (1998).
    [CrossRef]
  14. J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
    [CrossRef]
  15. J. B. Harris, T. W. Preist, J. R. Sambles, “Differential formalism for multilayer diffraction gratings made with uniaxial materials,” J. Opt. Soc. Am. A 12, 1965–1973 (1995).
    [CrossRef]
  16. J. B. Harris, T. W. Preist, E. L. Wood, J. R. Sambles, “Conical diffraction from multicoated gratings containing uniaxial materials,” J. Opt. Soc. Am. A 13, 803–810 (1996).
    [CrossRef]
  17. M. E. Inchaussandague, R. A. Depine, “Polarization conversion from diffraction gratings made of uniaxial crystals,” Phys. Rev. E 54, 2899–2911 (1996).
    [CrossRef]
  18. M. E. Inchaussandague, R. A. Depine, “Rigorous vector theory for diffraction from gratings made of biaxial crystals,” J. Mod. Opt. 44, 1–27 (1997).
    [CrossRef]
  19. E. Popov, M. Nevière, “Surface-enhanced second-harmonics generation in nonlinear corrugated dielectrics: new theoretical approaches,” J. Opt. Soc. Am. B 11, 1555–1564 (1994).
    [CrossRef]
  20. G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
    [CrossRef]
  21. 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]
  22. 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]
  23. G. Granet, J. Chandezon, “The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating,” Pure Appl. Opt. 6, 727–740 (1997).
    [CrossRef]
  24. S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
    [CrossRef]
  25. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  26. Ph. 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]
  27. 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]
  28. R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 9–11.
  29. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  30. L. Li, “On the matrix truncation in the modal methods of diffraction gratings,” paper presented at Electromagnetic Optics, the 19th Topical Meeting of the European Optical Society, Hyères, France, 7–9 September 1998.
  31. 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]

1998 (1)

1997 (5)

J.-P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
[CrossRef]

G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
[CrossRef]

M. E. Inchaussandague, R. A. Depine, “Rigorous vector theory for diffraction from gratings made of biaxial crystals,” J. Mod. Opt. 44, 1–27 (1997).
[CrossRef]

G. Granet, J. Chandezon, “The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating,” Pure Appl. Opt. 6, 727–740 (1997).
[CrossRef]

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

1996 (9)

L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
[CrossRef]

M. E. Inchaussandague, R. A. Depine, “Polarization conversion from diffraction gratings made of uniaxial crystals,” Phys. Rev. E 54, 2899–2911 (1996).
[CrossRef]

Ph. 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. B. Harris, T. W. Preist, E. L. Wood, J. R. Sambles, “Conical diffraction from multicoated gratings containing uniaxial materials,” J. Opt. Soc. Am. A 13, 803–810 (1996).
[CrossRef]

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]

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]

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

1995 (7)

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (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]

T. W. Preist, N. P. K. Cotter, J. R. Sambles, “Periodic multilayer gratings of arbitrary shape,” J. Opt. Soc. Am. A 12, 1740–1748 (1995).
[CrossRef]

J. B. Harris, T. W. Preist, J. R. Sambles, “Differential formalism for multilayer diffraction gratings made with uniaxial materials,” J. Opt. Soc. Am. A 12, 1965–1973 (1995).
[CrossRef]

G. Granet, “Analysis of diffraction by crossed gratings using a non-orthogonal coordinate system,” Pure Appl. Opt. 4, 777–793 (1995).
[CrossRef]

J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
[CrossRef]

G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
[CrossRef]

1994 (2)

1991 (1)

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

1986 (1)

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

1982 (1)

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]

1975 (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Bertoni, H. L.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Bryan-Brown, G. P.

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Chandezon, J.

G. Granet, J. Chandezon, “The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating,” Pure Appl. Opt. 6, 727–740 (1997).
[CrossRef]

G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
[CrossRef]

J.-P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
[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]

L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
[CrossRef]

G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
[CrossRef]

J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
[CrossRef]

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]

Cornet, G.

Cotter, N. P. K.

Coudert, O.

Depine, R. A.

M. E. Inchaussandague, R. A. Depine, “Rigorous vector theory for diffraction from gratings made of biaxial crystals,” J. Mod. Opt. 44, 1–27 (1997).
[CrossRef]

M. E. Inchaussandague, R. A. Depine, “Polarization conversion from diffraction gratings made of uniaxial crystals,” Phys. Rev. E 54, 2899–2911 (1996).
[CrossRef]

Dupuis, M. T.

Elston, S. J.

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Gaylord, T. K.

Granet, G.

G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121–1131 (1998).
[CrossRef]

G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
[CrossRef]

G. Granet, J. Chandezon, “The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating,” Pure Appl. Opt. 6, 727–740 (1997).
[CrossRef]

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]

L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
[CrossRef]

G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
[CrossRef]

J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
[CrossRef]

G. Granet, “Analysis of diffraction by crossed gratings using a non-orthogonal coordinate system,” Pure Appl. Opt. 4, 777–793 (1995).
[CrossRef]

Grann, E. B.

Guizal, B.

Harris, J. B.

Inchaussandague, M. E.

M. E. Inchaussandague, R. A. Depine, “Rigorous vector theory for diffraction from gratings made of biaxial crystals,” J. Mod. Opt. 44, 1–27 (1997).
[CrossRef]

M. E. Inchaussandague, R. A. Depine, “Polarization conversion from diffraction gratings made of uniaxial crystals,” Phys. Rev. E 54, 2899–2911 (1996).
[CrossRef]

Lalanne, Ph.

Li, L.

Mashev, L.

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

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.

Peng, S. T.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Petit, R.

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 9–11.

Plumey, J.-P.

J.-P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
[CrossRef]

L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
[CrossRef]

G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
[CrossRef]

J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, M. Nevière, “Surface-enhanced second-harmonics generation in nonlinear corrugated dielectrics: new theoretical approaches,” J. Opt. Soc. Am. B 11, 1555–1564 (1994).
[CrossRef]

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

Preist, T. W.

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.

Tamir, T.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Thorpe, R. N.

Wanstall, N. P.

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

Watts, R. A.

Wood, E. L.

IEEE Trans. Antennas Propag. (1)

J.-P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

J. Mod. Opt. (2)

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

M. E. Inchaussandague, R. A. Depine, “Rigorous vector theory for diffraction from gratings made of biaxial crystals,” J. Mod. Opt. 44, 1–27 (1997).
[CrossRef]

J. Opt. (Paris) (2)

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]

E. Popov, L. Mashev, “Conical diffraction mounting generalization of a rigorous differential method,” J. Opt. (Paris) 17, 175–180 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (15)

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994); Errata 13, 543 (1996).

G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121–1131 (1998).
[CrossRef]

J.-P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
[CrossRef]

G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
[CrossRef]

Ph. 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. B. Harris, T. W. Preist, E. L. Wood, J. R. Sambles, “Conical diffraction from multicoated gratings containing uniaxial materials,” J. Opt. Soc. Am. A 13, 803–810 (1996).
[CrossRef]

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]

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, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (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]

T. W. Preist, N. P. K. Cotter, J. R. Sambles, “Periodic multilayer gratings of arbitrary shape,” J. Opt. Soc. Am. A 12, 1740–1748 (1995).
[CrossRef]

J. B. Harris, T. W. Preist, J. R. Sambles, “Differential formalism for multilayer diffraction gratings made with uniaxial materials,” J. Opt. Soc. Am. A 12, 1965–1973 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. B (1)

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Phys. Rev. E (1)

M. E. Inchaussandague, R. A. Depine, “Polarization conversion from diffraction gratings made of uniaxial crystals,” Phys. Rev. E 54, 2899–2911 (1996).
[CrossRef]

Pure Appl. Opt. (4)

G. Granet, J.-P. Plumey, J. Chandezon, “Scattering by a periodically corrugated dielectric layer with non-identical faces,” Pure Appl. Opt. 4, 1–5 (1995).
[CrossRef]

L. Li, G. Granet, J.-P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996).
[CrossRef]

G. Granet, J. Chandezon, “The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating,” Pure Appl. Opt. 6, 727–740 (1997).
[CrossRef]

G. Granet, “Analysis of diffraction by crossed gratings using a non-orthogonal coordinate system,” Pure Appl. Opt. 4, 777–793 (1995).
[CrossRef]

Other (2)

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 9–11.

L. Li, “On the matrix truncation in the modal methods of diffraction gratings,” paper presented at Electromagnetic Optics, the 19th Topical Meeting of the European Optical Society, Hyères, France, 7–9 September 1998.

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.


Figures (3)

Fig. 1
Fig. 1

Notation and Cartesian coordinate system for a grating.

Fig. 2
Fig. 2

Definitions of the spatial domains D+, D-, D1, D2, and D0.

Fig. 3
Fig. 3

Multilayer approximation used in the FMM to treat a grating of arbitrary profile.

Tables (5)

Tables Icon

Table 1 Eigenvalues of Eq. (12) in Medium 1 for the Grating of Case A as Computed with the Truncation Order N = 11

Tables Icon

Table 2 Eigenvalues of Eq. (12) in Medium 2 for the Grating of Case A as Computed with the Truncation Order N = 11

Tables Icon

Table 3 Diffraction Efficienciesa of the Grating of Case A as Computed by the C Method with the Truncation Order N = 11

Tables Icon

Table 4 Diffraction Efficiencies of the Grating of Case B as Computed by the C Method and the FMM

Tables Icon

Table 5 Diffraction Efficiencies of the Grating of Case C as Computed by the C Method and the FMM

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

2x2+2y2+k02μF=0,
F=m Amp± expiαmx±iβmpy,  p=1, 2,
αm=n1k0 sin θ+mK,  K=2πd,
βmp=np2k02-αm21/2,  Reβmp+Imβmp>0,
v=x,  u=y-ax
x=vxv+uxu=v-a˙ u, y=vyv+uyu=u,
Lv, u; x=2v2-2a˙ 2vu-ä u+1+a˙22u2+k02pμ.
k02pμ+2v2001FF=iv a˙+a˙ v1+a˙210×1iuFF,
v  iα,  u  iρ,
βp2001FF=ρ-αa˙+a˙α1+a˙a˙10FF,
a˙mn=a˙m-n=1d0d a˙xexp-im-nKxdx,
-1βp2αa˙+a˙α1βp21+a˙a˙10FF=1ρFF.
F+=expiα0x-iβ01y+nU+expiαnx+iβn1yAn1+mexpiαmxqV+ Fmq+ expiρq+uCq+
F-=nU-expiαnx-iβn2yAn2+mexpiαmxqV- Fmq- expiρq-uCq-
F+=mexpiαmxLm-β01exp-iβ01u+nU+ Lm-nβn1expiβn1uAn1+qV+ Fmq+ expiρq+uCq+,
F-=mexpiαmx×kU- Lm-k-βk2exp-iβk2uAk2+rV- Fmr- expiρr-uCr-,
Lmγ=1d0dexpiγax-imKxdx.
Lm-β01+nU+ Lm-nβn1An1+qV+ Fmq+Cq+ =kU- Lm-k-βk2Ak2+rV- Fmr-Cr-.
FmnR+, Fmq+, -FmkR-, -Fmr-An1Cq+Ak2Cr-=-Fm0R,in,
FmnR+=Lm-n+βn1, FmkR-=Lm-k-βk2, Fm0R,in=Lm-β01.
t=xˆ+a˙xyˆ.
G=Ex+a˙Ey.
Ex=-Z0ik0Hzy,  Ey=Z0ik0Hzx,
G=Z0ik0a˙ Fv-1+a˙2Fu.
GmnR+, Gmq+, -GmkR-, -Gmr-An1Cq+Ak2Cr-=-Gm0R,in,
GmnR+=Z0k01sa˙m-sαs-1+a˙·a˙msβn1Ls-n+βn1, GmkR-=Z0k02sa˙m-sαs+1+a˙·a˙msβk2Ls-k-βk2, Gm0R, in=Z0k01sa˙m-sαs+1+a˙·a˙msβ01Ls-β01, Gmq+=Z0k01sa˙m-sαs-1+a˙·a˙msρq+Fsq+, Gmr-=Z0k02sa˙m-sαs-1+a˙·a˙msρr-Fsr-.
FmnR+Fmq+-FmkR--Fmr-GmnR+Gmq+-GmkR--Gmr-An1Cq+Ak2Cr-=-Fm0R,inGm0R,in.
ηnr=βn1β01 |An1|2
ηkt=2βk21β01 |Ak2|2
m1=-α0K-N-12, m2=-α0K+N-12,

Metrics