OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 596–603

Differential theory for anisotropic cylindrical objects with an arbitrary cross section

Philippe Boyer  »View Author Affiliations


JOSA A, Vol. 30, Issue 4, pp. 596-603 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000596


View Full Text Article

Enhanced HTML    Acrobat PDF (584 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We extend the differential theory to anisotropic cylindrical structures with an arbitrary cross section. Two cases have to be distinguished. When the anisotropic cylinders do not contain the origin, the scattering matrix of the device is calculated from the extended differential theory with the help of the scattering matrix propagation algorithm. The fields outside the cylinders are described by Fourier–Bessel expansions. When the origin is located in one cylinder, the fields inside the cylinder are expressed from a semi-analytical theory related to a homogeneous anisotropic medium. In this second case, the formalism of the scattering matrix propagation algorithm is not exactly the same and requires suitable change. The numerical results are in good agreement with the ones obtained for the diffraction by one circular cylinder. The theory is then applied on the diffraction by an elliptical cylinder.

© 2013 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(060.2310) Fiber optics and optical communications : Fiber optics
(160.1190) Materials : Anisotropic optical materials

ToC Category:
Diffraction and Gratings

History
Original Manuscript: December 11, 2012
Revised Manuscript: February 4, 2013
Manuscript Accepted: February 5, 2013
Published: March 11, 2013

Citation
Philippe Boyer, "Differential theory for anisotropic cylindrical objects with an arbitrary cross section," J. Opt. Soc. Am. A 30, 596-603 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-596


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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).
  2. M. Nevière and E. Popov, Light Propagation In Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).
  3. E. Popov and M. Nevière, “Grating theory: new equations in Fourier space leading to fast converging result in TM polarization,” J. Opt. Soc. Am. A 17, 1773–1784 (2000). [CrossRef]
  4. E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001). [CrossRef]
  5. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  6. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996). [CrossRef]
  7. S. Enoch, E. Popov, and M. Nevière, “3-D photonic crystals dispersion relation: improved convergence using fast Fourier factorization (FFF) method,” Proc. SPIE 4438, 183–190(2001). [CrossRef]
  8. S. Enoch, E. Popov, and N. Bonod, “Analysis of the physical origin of surface modes on finite size photonic crystals,” Phys. Rev. B 72, 155101 (2005). [CrossRef]
  9. N. Bonod, E. Popov, and M. Nevière, “Factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect,” Opt. Commun. 244, 389–398 (2005). [CrossRef]
  10. P. Boyer, E. Popov, M. Nevière, and G. Tayeb, “Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section,” J. Opt. Soc. Am. A 21, 2146–2153 (2004). [CrossRef]
  11. P. Boyer, E. Popov, M. Nevière, and G. Renversez, “Diffraction theory: application of the fast Fourier factorization to cylindrical devices with arbitrary cross lighted in conical mounting,” J. Opt. Soc. Am. A 23, 1146–1158 (2006). [CrossRef]
  12. P. Boyer, G. Renversez, E. Popov, and M. Nevière, “Improved differential method for microstructured optical fibres,” J. Opt. A 9, 728–740 (2007). [CrossRef]
  13. B. Stout, M. Nevière, and E. Popov, “Light diffraction by a three-dimensional object: differential theory,” J. Opt. Soc. Am. A 22, 2385–2404 (2005). [CrossRef]
  14. B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. part I: homogeneous sphere,” J. Opt. Soc. Am. A 23, 1111–1123 (2006). [CrossRef]
  15. B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. part II: arbitrary-shaped object—differential theory,” J. Opt. Soc. Am. A 23, 1124–1134 (2006). [CrossRef]
  16. M. Nevière, E. Popov, and P. Boyer, “Diffraction theory of an anisotropic circular cylinder,” J. Opt. Soc. Am. A 23, 1731–1740 (2006). [CrossRef]
  17. J. C. Monzon and N. J. Damaskos, “Two-dimensional scattering by homogeneous anisotropic rod,” IEEE Trans. Antennas Propag. 34, 1243–1249 (1986). [CrossRef]
  18. J. C. Monzon, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: a spectral approach,” IEEE Trans. Antennas Propag. 35, 670–682 (1987). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited