Abstract

Starting from the electromagnetic theory, we derive an asymptotic formalism to investigate the behavior of perfectly conducting gratings used at small wavelengths to groove pitch ratios and near normal incidence. The theory is applied to study three classical types of profiles: sinusoidal, lamellar, and blazed gratings. Results are given for both -1 and -2 Littrow (or near Littrow) mounts. The accuracy of the theory and the limits of the domain where it applies are studied by the use of rigorous electromagnetic computations. The role of a finite conductivity of the surface is also investigated.

© 1978 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Maystre, "Sur la Diffraction d'une onde plane par un réseau mé tallique de conductivite finie," Opt. Commun. 6, 50 (1972).
  2. M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).
  3. E. Loewen, M. Nevière, and D. Maystre, "Grating Efficiency Theory as it Applies to Blazed and Holographic Gratings," Appl. Opt. 16, 2711 (1977).
  4. B. A. Lippman, "Note on the Theory of Gratings," J. Opt. Soc. Am. 43, 408 (1953).
  5. R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).
  6. R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 65, 773 (1969).
  7. R. F. Millar, "Singularities of Two-Dimensional Exterior Solutions of the Helmholtz Equation," Proc. Camb. Philos. Soc. 69, 175 (1971).
  8. R.G. Barentsev, Vestn. Leningr. Univ. 1, 66 (1965).
  9. J. Pavageau, "Equation intégrale pour la diffraction electromagné tique par des conducteurs parfaits dans les problèmes à deux dimensions- Application aux ré seaux," C. R. Acad. Sci. Ser. B 264, 424 (1967).
  10. J. L. Uretsky, "The Scattering of Plane Waves from Periodic Surfaces," Ann. Phys. (Leipzig) 33, 400 (1965).
  11. A. Wirgin, "Considé rations thé oriques sur la diffraction par ré flexion sur des surfaces quasiment planes; application a la diffraction par des ré seaux," C. R. Acad. Sci. (Paris), 259, 1486 (1964).
  12. M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).
  13. R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).
  14. M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).
  15. R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 69, 217 (1971).
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.
  17. E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).
  18. D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).
  19. E. G. Loewen and M. Neviè re, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. (to be published).

1977 (1)

1974 (1)

M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).

1973 (1)

M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).

1972 (3)

D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).

D. Maystre, "Sur la Diffraction d'une onde plane par un réseau mé tallique de conductivite finie," Opt. Commun. 6, 50 (1972).

R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).

1971 (2)

R. F. Millar, "Singularities of Two-Dimensional Exterior Solutions of the Helmholtz Equation," Proc. Camb. Philos. Soc. 69, 175 (1971).

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 69, 217 (1971).

1970 (1)

M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).

1969 (1)

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 65, 773 (1969).

1967 (1)

J. Pavageau, "Equation intégrale pour la diffraction electromagné tique par des conducteurs parfaits dans les problèmes à deux dimensions- Application aux ré seaux," C. R. Acad. Sci. Ser. B 264, 424 (1967).

1966 (1)

R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).

1965 (2)

R.G. Barentsev, Vestn. Leningr. Univ. 1, 66 (1965).

J. L. Uretsky, "The Scattering of Plane Waves from Periodic Surfaces," Ann. Phys. (Leipzig) 33, 400 (1965).

1964 (1)

A. Wirgin, "Considé rations thé oriques sur la diffraction par ré flexion sur des surfaces quasiment planes; application a la diffraction par des ré seaux," C. R. Acad. Sci. (Paris), 259, 1486 (1964).

1953 (1)

Barentsev, R.G.

R.G. Barentsev, Vestn. Leningr. Univ. 1, 66 (1965).

Cadilhac, M.

M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).

M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).

R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.

Lippman, B. A.

Loewen, E.

Loewen, E. G.

E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).

E. G. Loewen and M. Neviè re, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. (to be published).

Maystre, D.

E. Loewen, M. Nevière, and D. Maystre, "Grating Efficiency Theory as it Applies to Blazed and Holographic Gratings," Appl. Opt. 16, 2711 (1977).

R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).

D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).

D. Maystre, "Sur la Diffraction d'une onde plane par un réseau mé tallique de conductivite finie," Opt. Commun. 6, 50 (1972).

E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).

Millar, R. F.

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 69, 217 (1971).

R. F. Millar, "Singularities of Two-Dimensional Exterior Solutions of the Helmholtz Equation," Proc. Camb. Philos. Soc. 69, 175 (1971).

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 65, 773 (1969).

Nevière, M.

E. Loewen, M. Nevière, and D. Maystre, "Grating Efficiency Theory as it Applies to Blazed and Holographic Gratings," Appl. Opt. 16, 2711 (1977).

M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).

M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).

M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).

E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).

E. G. Loewen and M. Neviè re, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. (to be published).

Pavageau, J.

J. Pavageau, "Equation intégrale pour la diffraction electromagné tique par des conducteurs parfaits dans les problèmes à deux dimensions- Application aux ré seaux," C. R. Acad. Sci. Ser. B 264, 424 (1967).

Petit, R.

M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).

M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).

R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).

D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).

R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).

Uretsky, J. L.

J. L. Uretsky, "The Scattering of Plane Waves from Periodic Surfaces," Ann. Phys. (Leipzig) 33, 400 (1965).

Vincent, P.

M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).

Wirgin, A.

A. Wirgin, "Considé rations thé oriques sur la diffraction par ré flexion sur des surfaces quasiment planes; application a la diffraction par des ré seaux," C. R. Acad. Sci. (Paris), 259, 1486 (1964).

Ann. Phys. (1)

J. L. Uretsky, "The Scattering of Plane Waves from Periodic Surfaces," Ann. Phys. (Leipzig) 33, 400 (1965).

Appl. Opt. (1)

C. R. Acad. Sci. (1)

A. Wirgin, "Considé rations thé oriques sur la diffraction par ré flexion sur des surfaces quasiment planes; application a la diffraction par des ré seaux," C. R. Acad. Sci. (Paris), 259, 1486 (1964).

C. R. Acad. Sci. Ser. B (2)

R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Ser. B 262, 468 (1966).

J. Pavageau, "Equation intégrale pour la diffraction electromagné tique par des conducteurs parfaits dans les problèmes à deux dimensions- Application aux ré seaux," C. R. Acad. Sci. Ser. B 264, 424 (1967).

IEEE Trans. Antennas Propag. (1)

M. Neviè re, M. Cadilhac, and R. Petit, "Applications of Conformal Mappings to the Diffraction of Electromagnetic Waves by a Grating," IEEE Trans. Antennas Propag. AP-21, 37 (1973).

J. Opt. Soc. Am. (1)

Nouv. Rev. Opt. (1)

M. Nevière, P. Vincent, and R. Petit, "Sur la theorie du réseaux conducteur et ses applications a l’optique," Nouv. Rev. Opt. 5, 65 (1974).

Opt. Commun. (3)

D. Maystre, "Sur la Diffraction d'une onde plane par un réseau mé tallique de conductivite finie," Opt. Commun. 6, 50 (1972).

D. Maystre and R. Petit, "Diffraction par un ré seau lamellaire infiniment conducteur," Opt. Commun. 5, 90 (1972).

M. Neviè re, M. Cadilhac, "Sur la Validité du Developement de Rayleigh," Opt. Commun. 2, 235 (1970).

Proc. Camb. Philos. Soc. (3)

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 65, 773 (1969).

R. F. Millar, "Singularities of Two-Dimensional Exterior Solutions of the Helmholtz Equation," Proc. Camb. Philos. Soc. 69, 175 (1971).

R. F. Millar, "On the Rayleigh Assumption in Scattering by a Periodic Surface," Proc. Camb. Philos. Soc. 69, 217 (1971).

Rev. Phys. Appl. (1)

R. Petit and D. Maystre, "Application des lois de l'é lectromagnetique a l'é tude des ré seaux," Rev. Phys. Appl. 7, 427 (1972).

Other (4)

R.G. Barentsev, Vestn. Leningr. Univ. 1, 66 (1965).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.

E. G. Loewen, M. Nevière and D. Maystre, "Efficiency Optimization of Rectangular Groove Gratings in Visible and IR Regions," (unpublished).

E. G. Loewen and M. Neviè re, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. (to be published).

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.