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Cylindrical Space Fourier-Bessel Mode solver for Maxwell’s Wave Equation

Received: 18 May 2013     Published: 30 June 2013
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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.

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

Keywords

Fourier-Bessel, Mode Solver, Photonic Crystal, Eigenmatrix, Photonic Quasi-Crystal

References
[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
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  • 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

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    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

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    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

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  • @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}
    }
    

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    AU  - Robert Claude Gauthier
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    JO  - Advances in Materials
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    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
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Author Information
  • Dept. of Electronics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

  • Dept. of Electronics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

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