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A Study on the Contribution of a Buffer Coated with a Perfect Conductor to Constructing Eigenmodes in Square HAPCF

Received: 21 January 2019    Accepted: 2 March 2019    Published: 20 March 2019
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Abstract

The finite element method (FEM) was carried out to investigate the eigenmodes of square hole-assisted photonic crystal fiber (HAPCF). The Krylov-Schur iteration method was applied to solve the large matrix eigen equation that resulted from FEM. HAPCF is conventional optical fiber with air holes added on the interface between the core and cladding. HAPCF is divided into two classes. One has a buffer coated with a perfect conductor and the other was constructed with the same buffer of the dielectric as the cladding. As a result, transverse magnetic (TM) and transverse electric (TE) spectra were described schematically with the transverse vector fields, the longitudinal scalar fields and their projected contour lines on the cross section of the fiber. The mode types could be determined mainly with the contour lines of the longitudinal scalar field on the cross section of HAPCF. It was found that the buffer coated with the perfect conductor has a great influence on the forming characteristics of the eigenmodes. From the spectra, it was identified that the TM transverse vector fields were almost perfectly constrained in the core area, but the transverse vector fields of TE modes were distributed over to the buffer layer. So, it was understood that more reliable analysis is possible when describing eigenmodes with these three kinds of spectra.

Published in Journal of Electrical and Electronic Engineering (Volume 7, Issue 1)
DOI 10.11648/j.jeee.20190701.15
Page(s) 36-41
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

Eigenmode, Buffer Layer, Perfect Conductor, Transverse Vector Field, Longitudinal Scalar Field, Contour Line, Spectra, Krylov-Schur Iteration

References
[1] Russel Philip St. John, “Photonic Crystal Fibers,” Science, Vol 299, No. 5605 pp 358-362, 2003.
[2] Jan Sporik, Miloslave Filka, Vladimir Tejkal, Pavel Reichert, “Principle of photonic crystal fibers,” Elektroevue, Vol. 2, No. 2, June 2011.
[3] JC Knight, TA Birks, P. St. J. Russell, Dale Atkin “All-silica single-mode optical fiber with photonic crystal cladding: Errata,” Optics Letters 22(7), 484-7, May 1997.
[4] X. Yu, P. Shum, M. Yan, J. Love “Numerical investigations of interstitial hole-assistant microstructured optical fiber,” Journal of Optical Electronics and Advanced Materials Vol. 8, No. 1, pp. 372-375, Feb. 2006.
[5] Yeong Min Kim “A study on the eigenmodes of a square PCF depending on wave numbers,” IEIE Transactions on Smart Processing & Computing Vol. 6, No. 5, 365-371, Oct. 2017.
[6] Yeong Min Kim, Se Jung Oh “A study on the Eigenmodes Constructed in the HAPCF,” HSST, Vol. 8, No. 11, pp. 223-233, Nov. 2018.
[7] C. J. Reddy, Manohar D. Deshpande, C. R. Cockrell, and Fred B. Beck, “Finite Element Method for Eigenvalue Problems in Electromagnetics,” NASA Technical Paper 3485, Dec. 1994.
[8] Peter P. Silvester and Ronald L. Ferrari, “Finite elements for Electrical Engineers 3rd ed.,” Cambridge University Press, App. 2, pp. 459-463, 1996.
[9] G. W. Stewart, “A Krylov Schur Algorithm for Large Eigenproblems” SIAM J. Matrix Anal. & Appl. Vol. 23, No. 3, pp. 601-614, 2002.
[10] Yeong Min Kim “A Study on the Eigen Modes of PCF Varying the Position of the Dielectric Holes by FEM,” Global Journal of Engineering Science and Researches, Vol. 3, No. 7, pp. 130-135, July 2016.
[11] V. Hernandez, J. E. Roman, A. Tomas, V. Vidal, “Arnoldi Methods in SLEPc,” SLEPc Technical Report STR-4 Available at http://www.grycap.upv.es/slepc
[12] David S. Watkins, “The QR Algorithm Revisited,” SIAM Review, Vol. 50, No. 1, pp. 133–145, Feb. 2008.
[13] Maysum Panju “Iterative Methods for Computing Eigenvalues and Eigenvectors” University of Waterloo, http://mathreview.uwaterloo.ca
[14] Rahul Kumar Meena, Himanshu Joshi, Ramesh Bharti, Khushbu Sharma “Design of Hybrid Photonic Crystal Fiber for Low Confinement Loss and Dispersion Shifted Fiber,” International Journal of Engineering and Applied Sciences (IJEAS), Volume-2, Issue-7, July 2015.
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  • APA Style

    Yeong Min Kim. (2019). A Study on the Contribution of a Buffer Coated with a Perfect Conductor to Constructing Eigenmodes in Square HAPCF. Journal of Electrical and Electronic Engineering, 7(1), 36-41. https://doi.org/10.11648/j.jeee.20190701.15

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    ACS Style

    Yeong Min Kim. A Study on the Contribution of a Buffer Coated with a Perfect Conductor to Constructing Eigenmodes in Square HAPCF. J. Electr. Electron. Eng. 2019, 7(1), 36-41. doi: 10.11648/j.jeee.20190701.15

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    AMA Style

    Yeong Min Kim. A Study on the Contribution of a Buffer Coated with a Perfect Conductor to Constructing Eigenmodes in Square HAPCF. J Electr Electron Eng. 2019;7(1):36-41. doi: 10.11648/j.jeee.20190701.15

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  • @article{10.11648/j.jeee.20190701.15,
      author = {Yeong Min Kim},
      title = {A Study on the Contribution of a Buffer Coated with a Perfect Conductor to Constructing Eigenmodes in Square HAPCF},
      journal = {Journal of Electrical and Electronic Engineering},
      volume = {7},
      number = {1},
      pages = {36-41},
      doi = {10.11648/j.jeee.20190701.15},
      url = {https://doi.org/10.11648/j.jeee.20190701.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20190701.15},
      abstract = {The finite element method (FEM) was carried out to investigate the eigenmodes of square hole-assisted photonic crystal fiber (HAPCF). The Krylov-Schur iteration method was applied to solve the large matrix eigen equation that resulted from FEM. HAPCF is conventional optical fiber with air holes added on the interface between the core and cladding. HAPCF is divided into two classes. One has a buffer coated with a perfect conductor and the other was constructed with the same buffer of the dielectric as the cladding. As a result, transverse magnetic (TM) and transverse electric (TE) spectra were described schematically with the transverse vector fields, the longitudinal scalar fields and their projected contour lines on the cross section of the fiber. The mode types could be determined mainly with the contour lines of the longitudinal scalar field on the cross section of HAPCF. It was found that the buffer coated with the perfect conductor has a great influence on the forming characteristics of the eigenmodes. From the spectra, it was identified that the TM transverse vector fields were almost perfectly constrained in the core area, but the transverse vector fields of TE modes were distributed over to the buffer layer. So, it was understood that more reliable analysis is possible when describing eigenmodes with these three kinds of spectra.},
     year = {2019}
    }
    

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    AU  - Yeong Min Kim
    Y1  - 2019/03/20
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    N1  - https://doi.org/10.11648/j.jeee.20190701.15
    DO  - 10.11648/j.jeee.20190701.15
    T2  - Journal of Electrical and Electronic Engineering
    JF  - Journal of Electrical and Electronic Engineering
    JO  - Journal of Electrical and Electronic Engineering
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    UR  - https://doi.org/10.11648/j.jeee.20190701.15
    AB  - The finite element method (FEM) was carried out to investigate the eigenmodes of square hole-assisted photonic crystal fiber (HAPCF). The Krylov-Schur iteration method was applied to solve the large matrix eigen equation that resulted from FEM. HAPCF is conventional optical fiber with air holes added on the interface between the core and cladding. HAPCF is divided into two classes. One has a buffer coated with a perfect conductor and the other was constructed with the same buffer of the dielectric as the cladding. As a result, transverse magnetic (TM) and transverse electric (TE) spectra were described schematically with the transverse vector fields, the longitudinal scalar fields and their projected contour lines on the cross section of the fiber. The mode types could be determined mainly with the contour lines of the longitudinal scalar field on the cross section of HAPCF. It was found that the buffer coated with the perfect conductor has a great influence on the forming characteristics of the eigenmodes. From the spectra, it was identified that the TM transverse vector fields were almost perfectly constrained in the core area, but the transverse vector fields of TE modes were distributed over to the buffer layer. So, it was understood that more reliable analysis is possible when describing eigenmodes with these three kinds of spectra.
    VL  - 7
    IS  - 1
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Author Information
  • Electronic Physics, Kyonggi University, Gyeonggi-do, Republic of Korea

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