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