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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 4 — Apr. 1, 1978
  • pp: 490–495

A new general integral theory for dielectric coated gratings

D. Maystre  »View Author Affiliations

JOSA, Vol. 68, Issue 4, pp. 490-495 (1978)

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We present a new rigorous integral formalism for the theoretical study of dielectric coated gratings and grating couplers. It applies in the resonance domain, where the wavelength of the incident field and the groove spacing are of the same order of magnitude. The computed program issued from this theory extends the domain of application of the previous differential or integral theories. It can be used to investigate, with a very good accuracy, the properties of bare or dielectric coated gratings, for any groove shape and any polarization, in the entire visible, ultraviolet, and infrared regions. Various classical criteria are used to control the validity of the numerical results and comparisons are made with the numerical results obtained using the previous integral and differential formalisms. Two examples of applications are given. First, we show that the new possibilities of our program lead to a better agreement between theoretical results and experimental data. Second, a theoretical study of a certain type of grating coupler is given.

© 1978 Optical Society of America

D. Maystre, "A new general integral theory for dielectric coated gratings," J. Opt. Soc. Am. 68, 490-495 (1978)

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  1. R. Petit, "Electromagnetic grating theories: limitations and successes," Nouv. Rev. Opt. 3, 129–135 (1975).
  2. A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar periodic structures," Alta Freq., 38, special issue on URSI Symposium, 282–285 (1968).
  3. P. M. Van den Berg, "Rigorous diffraction theory of optical reflexion and transmission gratings," thesis (Report No. 1971-16, Delft, Netherlands, 1971).
  4. D. Maystre, "Sur la diffraction d'une onde plane par un réseau mé- tallique de conductivité finie," Opt. Commun. 1, 50–54 (1972).
  5. D. Maystre, "Sur la diffraction d'une onde plane électromagnétique par un réseau métallique," Opt. Commun. 3, 216–219 (1973).
  6. R. Petit, D. Maystre, and M. Nevière, "Practical applications of the electromagnetic theory of gratings," Space Optics, Proceedings of the Ninth International Congress of the I.C.O., 667–681 (1972).
  7. D. Maystre, R. Petit, M. Duban, and J. Gilewicz, "Theoretical determination of the efficiencies for a conducting grating used in the near ultraviolet," Nouv. Rev. Opt. 2, 79–85 (1974).
  8. D. Maystre, "Sur la diffraction et l'absorption par les réseaux utilisés dans l'infraroige, le visible et l'ultraviolet," thesis (University Aix-Marseille III, CNRS A.O. 9545, 1974) (unpublished).
  9. D. Maystre and R. Petit, "Some recent theoretical results for gratings; Application tcqtheir use in the very far ultraviolet," Nouv. Rev. Opt. 3, 165–180 (1976).
  10. E. G. Loewen, M. Nevière, and D. Maystre, "Review of grating efficiency theory as it applies to blazed and holographic gratings," Appl. Opt. (to be published).
  11. R. C. McPhedran and D. Maystre, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Opt. Acta 5, 413–421 (1974).
  12. R. C. McPhedran and D. Maystre, "Theoretical study of the diffraction anomalies of holographic gratings," Nouv. Rev. Opt. 4, 241–248 (1974).
  13. E. G. Loewen, D. Maystre, R. C. McPhedran, and I. Wilson, "Correlation between efficiency of diffraction gratings and theoretical calculations over a wide range," Jpn. J. Appl. Phys. 14 (suppl.), 143–155 (1975).
  14. G. Cerutti-Maori, R. Petit, and M. Cadilhac, "Etude numérique du champ diffracté par un réseau," C. R. Acad. Sci. Paris 268, 1060–1063 (1969).
  15. M. Nevière, P. Vincent, and R. Petit, "Theory of conducting gratings and their applications to optics," Nouv. Rev. Opt. 2, 65–77 (1974).
  16. M. Nevière; "Sur un formalisme diffèrentiel pour les problames de diffraction dans le domaine de résonance," thesis (University Aix-Marseille III, CNRS A.O. 11556, 1975) (unpublished).
  17. M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, and P. Vincent, "Presentation and verification of a differential formulation for the diffraction by conducting gratings," Nouv. Rev. Opt. 2, 87–95 (1975).
  18. M. Nevière, P. Vincent, R. Petit, and M. Cadilhac, "Determination of the coupling coefficient of a holographic thin film coupler," Opt. Commun. 3, 240–245 (1973).
  19. C. Müller, Foundations of the mathematical theory of electromagnetic waves (Springer Verlag, Berlin, 1969), p. 328.
  20. The linear vector space R0 of distributions, used in this paper, is the set of the linear continuous functionals on the space R0 of the functions ξ(x,y) defined by the following: ξ(x,y) is differentiable everywhere any number of times; ξ(x,y) is periodic with respect to x, with period d; ξ(x,y) is equal to zero outside a bounded segment of Oy axis. Using the Dirac notation, theδ function of R0 is defined by δξ, (x,y), = ξ(0,0).
  21. 21D. Maystre and R. Petit, "Application des propriétes des réseaux échelettes au filtrage des longueurs d'onde," Opt. Commun. 5, 380–382 (1972).
  22. D. Maystre and M. Nevière; "Quantitative theoretical study on the plasmon anomalies of diffraction gratings," J. Opt. 8, 165–174 (1977).
  23. J. Meixner, "On the behaviour of the electromagnetic fields at edges," IEEE Trans. Antennas Propag. 20, 422–447 (1972).
  24. D. Maystre, R. C. McPhedran, "Le théorème de réciprocité pour les réseaux de conductivité finie: démonstration et applications," Opt. Commun. 2, 164–167 (1974).
  25. M. Nevière, M. Cadilhac, and R. Petit, "Applications of conformal mappings to the diffraction of electromagnetic waves by a grating," IEEE Trans. Antennas Propag. 21, 37–46 (1973).
  26. D. Maystre and R. Petit, "Brewster incidence for metallic gratings," Opt. Commun. 2, 196–200 (1976).
  27. M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 3, 431–436 (1976).
  28. A. Otto and W. Sohler, "Modification of the total reflectance modes in a dielectric film by one metal boundary," Opt. Commun. 3, 254–258 (1971).

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