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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9978–9990

Coordinate transformation formulation of electromagnetic scattering from imperfectly periodic surfaces

Koki Watanabe, Jaromír Pištora, and Yoshimasa Nakatake  »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 9978-9990 (2012)

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This paper considers the electromagnetic scattering problem of periodically corrugated surface with local imperfection of structural periodicity, and presents a formulation based on the coordinate transformation method (C-method). The C-method is originally developed to analyze the plane-wave scattering from perfectly periodic structures, and uses the pseudo-periodic property of the fields. The fields in imperfectly periodic structures are not pseudo-periodic and the C-method cannot be directly applied. This paper introduces the pseudo-periodic Fourier transform to convert the fields in imperfectly periodic structures to pseudo-periodic ones, and the C-method becomes then applicable.

© 2012 OSA

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

Original Manuscript: January 3, 2012
Revised Manuscript: March 8, 2012
Manuscript Accepted: March 8, 2012
Published: April 17, 2012

Koki Watanabe, Jaromír Pištora, and Yoshimasa Nakatake, "Coordinate transformation formulation of electromagnetic scattering from imperfectly periodic surfaces," Opt. Express 20, 9978-9990 (2012)

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  1. T. Oonishi, T. Konishi, and K. Itoh, “Fabrication of phase only binary blazed grating with subwavelength structures designed by deterministic method based on electromagnetic analysis,” Jpn. J. Appl. Phys.46, 5435–5440 (2007). [CrossRef]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Modeling the Flow of Light (Princeton Univ. Press, Princeton, 1995).
  3. C. Yang, K. Shi, P. Edwards, and Z. Liu, “Demonstration of a PDMS based hybrid grating and Fresnel lens (G-Fresnel) device,” Opt. Express18, 23529–23534 (2010). [CrossRef] [PubMed]
  4. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am.72, 839–846 (1982). [CrossRef]
  5. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980). [CrossRef]
  6. K. Watanabe and K. Yasumoto, “Two-dimensional electromagnetic scattering of non-plane incident waves by periodic structures,” Prog. Electromagnetic Res.PIER 74, 241–271 (2007). [CrossRef]
  7. K. Watanabe, J. Pištora, and Y. Nakatake, “Rigorous coupled-wave analysis of electromagnetic scattering from lamellar grating with defects,” Opt. Express19, 25799–25811 (2011). [CrossRef]
  8. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am.68, 1206–1210 (1978). [CrossRef]
  9. M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1385–1392 (1982). [CrossRef]
  10. E. Popov, M. Nevière, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A19, 33–42 (2002). [CrossRef]
  11. K. Watanabe, “Numerical integration schemes used on the differential theory for anisotropic gratings,” J. Opt. Soc. Am. A19, 2245–2252 (2002). [CrossRef]
  12. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A13, 1870–1876 (1996). [CrossRef]
  13. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  14. H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publ. RIMS, Kyoto Univ.9, 721–741 (1974). [CrossRef]
  15. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic Press, New York, 1984).

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