Volume 2, Issue 3, June 2013, Page: 32-35
Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation
Robert Claude Gauthier, Dept. of Electronics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Mohammed Alzahrani, Dept. of Electronics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Received: May 18, 2013;       Published: Jun. 30, 2013
DOI: 10.11648/j.am.20130203.12      View  3257      Downloads  186
Abstract
A Fourier-Bessel basis set in cylindrical coordinates is used to cast Maxwell’s wave equations into an eigenvalue problem from which the steady states of rotationally symmetric photonic structures can be determined. The rotational symmetry of the structure significantly reduces the order of the matrix making an efficient computation process that can be accommodated by desk top computers running MATLAB ©. In addition the matrix can be tuned to a particular mode profile type such as monopoles, dipoles, … enabling the user to target the desired mode features in the computations. The technique is applied to solving for the states of three different photonic structures; 12-fold quasi-crystal, silicon ring resonator and photonic crystal fiber. The particular features of a modal state are easily obtained by examining the eigenvector.
Keywords
Fourier-Bessel, Mode Solver, Photonic Crystal, Eigenmatrix, Photonic Quasi-Crystal
To cite this article
Robert Claude Gauthier, Mohammed Alzahrani, Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation, Advances in Materials. Vol. 2, No. 3, 2013, pp. 32-35. doi: 10.11648/j.am.20130203.12
Reference
[1]
S. Johnson and J. Joannopoulos, "Photonic crystals; The road from theory to practice," Kluwer Academic Publishers, Boston, 2002, pp. 20, 46.
[2]
R. Gauthier and K. Mnaymneh, "Photonic band gap properties of 12-fold quasi-crystal determined through FDTD analysis," Opt. Express 13, 1985-1998 (2005).
[3]
X. Qianfan, D. Fattal and R. G. Beausoleil, "Silicon microring resonators with 1.5-μm radius," Optics Express, Vol. 16 Issue 6, pp.4309-4315 (2008).
[4]
T. A. Birks , J. C. Knight, P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, pp. 961-963 (1997).
[5]
" This is not a reference. It is the web address of the journal." http://www.sciencepublishinggroup.com/journal/guideforauthors.aspx?journalid=129
Browse journals by subject