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. 31, Iss. 4 — Apr. 1, 2014
  • pp: 667–676

Mode solver based on Gegenbauer polynomial expansion for cylindrical structures with arbitrary cross sections

Kofi Edee, Mira Abboud, Gérard Granet, Jean Francois Cornet, and Nikolay A. Gippius  »View Author Affiliations


JOSA A, Vol. 31, Issue 4, pp. 667-676 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000667


View Full Text Article

Enhanced HTML    Acrobat PDF (592 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a modal method for the computation of eigenmodes of cylindrical structures with arbitrary cross sections. These modes are found as eigenvectors of a matrix eigenvalue equation that is obtained by introducing a new coordinate system that takes into account the profile of the cross section. We show that the use of Hertz potentials is suitable for the derivation of this eigenvalue equation and that the modal method based on Gegenbauer expansion (MMGE) is an efficient tool for the numerical solution of this equation. Results are successfully compared for both perfectly conducting and dielectric structures. A complex coordinate version of the MMGE is introduced to solve the dielectric case.

© 2014 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.7370) Optical devices : Waveguides

ToC Category:
Optical Devices

History
Original Manuscript: November 15, 2013
Revised Manuscript: January 17, 2014
Manuscript Accepted: January 24, 2014
Published: March 3, 2014

Citation
Kofi Edee, Mira Abboud, Gérard Granet, Jean Francois Cornet, and Nikolay A. Gippius, "Mode solver based on Gegenbauer polynomial expansion for cylindrical structures with arbitrary cross sections," J. Opt. Soc. Am. A 31, 667-676 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-667


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Edee, “Modal method based on subsectional Gegenbauer polynomial expansion for lamellar grating,” J. Opt. Soc. Am. A 28, 2006–2013 (2011). [CrossRef]
  2. K. Edee, I. Fenniche, G. Granet, and B. Guizal, “Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings: Weithing function, convergence and stability,” Prog. Electromagn. Res. 133, 17–35 (2013). [CrossRef]
  3. K. Edee and B. Guizal, “Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates implementation,” J. Opt. Soc. Am. A 30, 631–639 (2013). [CrossRef]
  4. M. Nevière and E. Popov, “New theoretical method for electromagnetic wave diffraction by a metallic or dielectric cylinder, bare coated with a thin dielectric layer,” J. Electromagn. Waves. Appl. 12, 1265–1296 (1998). [CrossRef]
  5. B. Sieger, “Die beugung einer ebenen elektrischen welle an einem schirm von elliptischem querscnitt,” Ann. Phys. 332, 626–664 (1908). [CrossRef]
  6. P. M. Morse and P. J. Rubenstein, “The diffraction of waves by ribbons and by slits,” Phys. Rev. 54, 895–898 (1938). [CrossRef]
  7. C. Yeh, “The diffraction of waves by a penetrable ribbon,” J. Math. Phys. 4, 65–71 (1963). [CrossRef]
  8. C. Yeh, “Scattering of obliquely incident light waves by elliptical fibers,” J. Opt. Soc. Am. 54, 1227–1281 (1964). [CrossRef]
  9. J.-T. Zhange and Y.-L. Li, “A new research approach of electromagnetic theory and its applications,” Indian J. Radio Space Phys. 35, 249–252 (2008).
  10. Y.-L. Li, J.-Y. Huang, M.-J. Wang, and J. T. Zhang, “Scattering field for the ellipsoidal targets irradiated by an electromagnetic wave with arbitrary polarizing and propagating direction,” Prog. Electromagn. Res. Lett. 1, 221–235 (2008). [CrossRef]
  11. Y.-L. Li, M.-J. Wang, and G.-F. Tang, “The scattering from an elliptic cylinder irradiated by an electromagnetic wave with arbitrary direction and polarization,” Prog. Electromagn. Res. Lett. 5, 137–149 (2008). [CrossRef]
  12. L. A. Ferrari, “Scale transformation of Maxwell’s equations and scattering by an elliptic cylinder,” J. Opt. Soc. Am. A 28, 1285–1290 (2011). [CrossRef]
  13. G. Granet, K. Edee, and D. Felbacq, “Scattering of a plane wave by rough surfaces: a new curvilinear coordinate system based approach,” Prog. Electromagn. Res. 41, 235–250 (2003).
  14. K. Edee, B. Guizal, G. Cranet, and A. Moreau, “Beam implementation in a nonorthogonal coordinate system: application to the scattering from random rough surfaces,” J. Opt. Soc. Am. A 25, 796–804 (2008). [CrossRef]
  15. K. Edee, J.-P. Plumey, and J. Chandezon, “On the Rayleigh–Fourier method and the Chandezon method: comparative study,” Opt. Commun. 286, 34–41 (2013). [CrossRef]
  16. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970), pp. 771–792.

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.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited