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.
| Published in | Advances in Materials (Volume 2, Issue 3) |
| DOI | 10.11648/j.am.20130203.12 |
| Page(s) | 32-35 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2013. Published by Science Publishing Group |
Fourier-Bessel, Mode Solver, Photonic Crystal, Eigenmatrix, Photonic Quasi-Crystal
| [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 |
APA Style
Robert Claude Gauthier, Mohammed Alzahrani. (2013). Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation. Advances in Materials, 2(3), 32-35. https://doi.org/10.11648/j.am.20130203.12
ACS Style
Robert Claude Gauthier; Mohammed Alzahrani. Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation. Adv. Mater. 2013, 2(3), 32-35. doi: 10.11648/j.am.20130203.12
AMA Style
Robert Claude Gauthier, Mohammed Alzahrani. Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation. Adv Mater. 2013;2(3):32-35. doi: 10.11648/j.am.20130203.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.am.20130203.12,
author = {Robert Claude Gauthier and Mohammed Alzahrani},
title = {Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation},
journal = {Advances in Materials},
volume = {2},
number = {3},
pages = {32-35},
doi = {10.11648/j.am.20130203.12},
url = {https://doi.org/10.11648/j.am.20130203.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.am.20130203.12},
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.},
year = {2013}
}
TY - JOUR T1 - Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation AU - Robert Claude Gauthier AU - Mohammed Alzahrani Y1 - 2013/06/30 PY - 2013 N1 - https://doi.org/10.11648/j.am.20130203.12 DO - 10.11648/j.am.20130203.12 T2 - Advances in Materials JF - Advances in Materials JO - Advances in Materials SP - 32 EP - 35 PB - Science Publishing Group SN - 2327-252X UR - https://doi.org/10.11648/j.am.20130203.12 AB - 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. VL - 2 IS - 3 ER -
Email: