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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 12, Iss. 12 — Dec. 1, 1995
  • pp: 2672–2678

Electromagnetic theory of Bragg–Fresnel linear zone plates

F. Montiel and M. Nevière  »View Author Affiliations

JOSA A, Vol. 12, Issue 12, pp. 2672-2678 (1995)

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An electromagnetic analysis of diffraction by Fresnel linear zone plates ruled into a homogeneous or a stratified media is developed. It takes advantage of the new possibilities brought by the introduction of the R-matrix propagation algorithm into the theory of lamellar gratings, namely, the large increase of the stability domain of the numerical results. Thus a linear Fresnel zone plate can be delt with as a period of such a grating, and the diffracted field can be computed for both TE and TM polarizations. Numerical examples show the convergence of the method and study the focusing properties of positive and negative zone plates. The influence of different parameters such as incidence or number of lines is pointed out.

© 1995 Optical Society of America

Original Manuscript: December 20, 1994
Revised Manuscript: May 15, 1995
Manuscript Accepted: June 15, 1995
Published: December 1, 1995

F. Montiel and M. Nevière, "Electromagnetic theory of Bragg–Fresnel linear zone plates," J. Opt. Soc. Am. A 12, 2672-2678 (1995)

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  1. V. V. Aristov, A. I. Erko, V. V. Martinov, “Principles of Bragg–Fresnel multilayer optics,” Rev. Phys. Appl. 23, 1623–1630 (1988);S. Babin, A. Erko, “Fabrication of diffractive x-ray optical elements,” Nucl. Instrum. Methods Phys. Res. A 282, 529–535 (1989). [CrossRef]
  2. J. Maser, “Evaluation of the efficiency of zones plates with high aspect ratios by application of coupled wave theory,” in X-ray Microscopy III, A. G. Michette, G. R. Morrison, G. J. Buckley, eds. (Springer-Verlag, Berlin, 1992), pp. 104–106. [CrossRef]
  3. A. Sammar, J.-M. André, “Diffraction of multilayer gratings and zone plates in the x-ray region using the Born approximation,” J. Opt. Soc. Am. A 10, 600–613 (1993). [CrossRef]
  4. A. Sammar, J.-M. André, “Dynamical theory of stratified Fresnel linear zone plates,” J. Opt. Soc. Am. A 10, 2324–2337 (1993);A. Mirone, M. Idir, P. Dhez, G. Soullie, A. Erko, “Dynamical theory for Bragg–Fresnel multilayer lenses for X-UV and X-ray range,” Opt. Commun. 111, 191–198 (1994). [CrossRef]
  5. R. Petit, Electromagnetic Theory of Gratings, (Springer-Verlag, Berlin, 1980). [CrossRef]
  6. J. T. Sheridan, C. J. R. Sheppard, “Coherent imaging of thick fine isolated structures,” J. Opt. Soc. Am. A 10, 614–632 (1993). [CrossRef]
  7. L. Li, “A multilayer modal method for diffraction gratings of arbitrary profile, depth, and conductivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993). [CrossRef]
  8. F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 3241–3250 (1994). [CrossRef]
  9. A. E. Sammar, “Etude théorique et expérimentale de systèmes optiques interférentiels dispersifs et focalisants pour la spectroscopie et l’imagerie x,” Ph.D. dissertation (Université Pierre et Marie Curie, Paris, May6, 1993).
  10. J. P. Hugonin, R. Petit, “A numerical study of the problem of diffraction at a non-periodic obstacle,” Opt. Commun. 20, 360–364 (1977);J. P. Hugonin, R. Petit, “Theoretical and numerical study of a locally deformed stratified medium,” J. Opt. Soc. Am. 71, 664–674 (1981). [CrossRef]
  11. M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications ὰ l’optique,” Nouv. Rev. Opt. 5, 65–77 (1974). [CrossRef]
  12. M. Nevière, J. Flamand, “Electromagnetic theory as it applies to x-ray and XUV gratings,” Nucl. Instrum. Methods 172, 273–279 (1980). [CrossRef]
  13. M. Nevière, J. Flamand, J. M. Lerner, “Optimization of gratings for soft x-ray monochromators,” Nucl. Instrum. Methods 195, 183–189 (1982). [CrossRef]
  14. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980). [CrossRef]
  15. J. W. Goodman, Introduction ὰ l’Optique de Fourier et à l’Holographie (Masson, Paris, 1972), p. 31

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