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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 71, Iss. 6 — Jun. 1, 1981
  • pp: 664–674

Theoretical and numerical study of a locally deformed stratified medium

J. P. Hugonin and R. Petit  »View Author Affiliations


JOSA, Vol. 71, Issue 6, pp. 664-674 (1981)
http://dx.doi.org/10.1364/JOSA.71.000664


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Abstract

The propagation of electromagnetic waves in the presence of a locally two-dimensional deformed plane waveguide is considered. We are concerned with the conversion of an incident beam into a guided beam as well as with the interaction of a guided beam with a local deformation. We look for a rigorous solution of Maxwell’s equations, i.e., a solution in which the errors depend only on the numerical methods used for evaluation. We outline the mathematical aspect of this rather formidable problem and emphasize the numerical difficulties that we have to overcome. An example is presented to give an idea of the capabilities of our computer program.

© 1981 Optical Society of America

Citation
J. P. Hugonin and R. Petit, "Theoretical and numerical study of a locally deformed stratified medium," J. Opt. Soc. Am. 71, 664-674 (1981)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-71-6-664


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References

  1. J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a non-periodic obstacle," Opt. Commun. 20, 360 (1977).
  2. J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a locally deformed plane waveguide," Opt. Commun. 22, 221 (1977).
  3. M. C. Hutley et al., "Presentation and verification of a differential formulation for the diffraction by conducting gratings," Nouv. Rev. Opt. 6, 87–95 (1975).
  4. R. Petit, Electromagnetic Theory of Gratings, Petit, ed. (Springer-Verlag, Berlin, 1980).
  5. Throughout the paper, when a is real and negative, √a means i√-a.
  6. Since Fourier transforms are defined as in distribution theory, the integral notation is purely formal.
  7. If, for example, the incident field is a plane wave in normal incidence [Ei = exp (-iy)], EDI(ζ)contains a term in δ(ζ).
  8. Let us recall that ζT = 1 implies that T = P(1/ζ) + aδ(ζ), where a is an arbitrary constant.
  9. P[iu/g (ζ)] is the distribution that, to any test function ø (ζ) assigns (equations) where IEpislon; is the set defined by (equations).
  10. The Fourier transform of (equations), where P(1/ζ) is the principal value distribution.
  11. P. Vincent, "Singularity expansions for cylinders of finite conductivity," Appl. Phys. 17, 239–248 (1978).
  12. We do not set in boldface letters that, like C, represent elements of an abstract vector space.
  13. There is no possible confusion between the operator D and the rectangular domain that appears in Fig. 1.
  14. The letters topped by the inverted-wedge sign are used for data (functions or constants) related to a given practical problem.
  15. J. Van Bladel, Electromagnetic Fields (McGraw-Hill, New York, 1964), p. 252.
  16. P. Vincent and M. Neviere, "The reciprocity theorm for corrugated surfaces used in conical diffraction mountings," Opt. Acta 26, 889–898 (1979).
  17. J. P. Hugonin, "On the numerical study of the deformed dielectric waveguide," presented at the international Union Radio Scientifique Internationale Symposium, Munich, 1980.
  18. More generally, the use of an approximation of L-1 is likely to increase the speed of convergence of the process.

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