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Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure

Received: 06 August 2013    Accepted:     Published: 20 September 2013
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Abstract

A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the Fourier-Bessel technique is highly suited for extracting the localized modes as it can be tuned to solve for a particular mode order. The possibility of using the circular structure as the defect region of a hexagonal array is also examined by studying the localized states obtained in a heterostructure configuration.

DOI 10.11648/j.optics.20130205.11
Published in Optics (Volume 2, Issue 5, October 2013)
Page(s) 51-60
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), 2024. Published by Science Publishing Group

Keywords

Photonic Quasi-Crystal, Fourier-Bessel, Steady States, Heterostructure, Circular Symmetric Mode Solver, Eigenvalue Method

References
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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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  • APA Style

    Scott Ronald. Newman, Robert Claude. Gauthier. (2013). Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure. Optics, 2(5), 51-60. https://doi.org/10.11648/j.optics.20130205.11

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    ACS Style

    Scott Ronald. Newman; Robert Claude. Gauthier. Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure. Optics. 2013, 2(5), 51-60. doi: 10.11648/j.optics.20130205.11

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    AMA Style

    Scott Ronald. Newman, Robert Claude. Gauthier. Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure. Optics. 2013;2(5):51-60. doi: 10.11648/j.optics.20130205.11

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  • @article{10.11648/j.optics.20130205.11,
      author = {Scott Ronald. Newman and Robert Claude. Gauthier},
      title = {Fourier-Bessel Analysis of Polar Space Symmetric Photonic Crystal; Resonator Modes and Heterostructure},
      journal = {Optics},
      volume = {2},
      number = {5},
      pages = {51-60},
      doi = {10.11648/j.optics.20130205.11},
      url = {https://doi.org/10.11648/j.optics.20130205.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.optics.20130205.11},
      abstract = {A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the Fourier-Bessel technique is highly suited for extracting the localized modes as it can be tuned to solve for a particular mode order. The possibility of using the circular structure as the defect region of a hexagonal array is also examined by studying the localized states obtained in a heterostructure configuration.},
     year = {2013}
    }
    

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    AB  - A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the Fourier-Bessel technique is highly suited for extracting the localized modes as it can be tuned to solve for a particular mode order. The possibility of using the circular structure as the defect region of a hexagonal array is also examined by studying the localized states obtained in a heterostructure configuration.
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    IS  - 5
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