Abstract

The work presented here focuses on the numerical modeling of cylindrical structure eigenmodes with an arbitrary cross section using Gegenbauer polynomials. The new eigenvalue equation leads to considerable reduction in computation time compared to the previous formulation. The main idea of this new formulation involves considering that the numerical scheme can be partially separated into two independent parts and the size of the eigenvalue matrix equation may be reduced by a factor of 2. We show that the ratio of the computation times between the first and current versions follows a linear relation with respect to the number of polynomials.

© 2014 Optical Society of America

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
J. Opt. Soc. Am. A 31(4) 667-676 (2014)

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating

K. Edee and J. P. Plumey
J. Opt. Soc. Am. A 32(3) 402-410 (2015)

Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates implementation

Kofi Edee and Brahim Guizal
J. Opt. Soc. Am. A 30(4) 631-639 (2013)

Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings

Kofi Edee
J. Opt. Soc. Am. A 28(10) 2006-2013 (2011)

Efficient implementation of B-spline modal method for lamellar gratings

Gérard Granet
J. Opt. Soc. Am. A 31(2) 332-337 (2014)