Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal

Ouarda Barkat

doi:doi:10.11648/j.jeee.20150302.11

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Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal

Ouarda Barkat

Published in Journal of Electrical and Electronic Engineering (Volume 3, Issue 2)

Received: 11 February 2015 Accepted: 5 March 2015 Published: 10 March 2015

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Abstract

In this work, we demonstrate via numerical simulation the general design for one dimensional photonic crystal (1D- PC). In the design procedure, the transfer matrix method and Bloch theorem are used to determine the transmission coefficient and dispersion relation of (1D- PC) structure for both TE (transverse electric) and TM (transverse magnetic) modes. Results obtained showing the effect of the filling factor as well as the incident angle on the photonic band gap width. The analysis is carried out using MATLAB software tool. The accuracy of the analysis is tested by comparing the computed results with measurements published data.

Published in	Journal of Electrical and Electronic Engineering (Volume 3, Issue 2)
DOI	10.11648/j.jeee.20150302.11
Page(s)	12-18
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 Band Gap, Transfer Matrix Method, Bloch Theorem, Transmission, Dispersion

References

[1]	H. Oraizi A. Abdolali, "Several theorems for reflection and transmission coefficients of plane wave incidence on planar multilayer metamaterial structures", IET Microw. Antennas Propag., Vol. 4, Iss. 11, pp. 1870–1879, 2010.
[2]	I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Complete band gaps in one-dimensional left-handed periodic structures," Physical Review Letters, Vol. 95, pp. 1-4, 2005.
[3]	Z. Wang, D. Liu "A few points on omnidirectional band gaps in one- dimensional photonic crystals," Applied Physics B, Appl. Phys. B 86, pp 473–476, 2007.
[4]	A. Gharaati and Z. Zare, "Photonic band structures and enhancement of omnidirectional reflection bands by using a ternary 1D photonic crystal including left-handed materials", Progress In Electromagnetics Research M, Vol. 20, pp 81-94, 2011.
[5]	S. K. Srivastava, and S. P. Ojha, "Enhancement of omnidirectional reflection bands in one-dimensional photonic crystals with left-handed materials," Progress In Electromagnetics Research, Vol. 68, pp 91-111, 2007.
[6]	Sakoda K: Optical properties of Photonic Crystals. New York: Springer Berlin Heidlberg; 2005.
[7]	M. Skorobogatiy, and J. Yang, Fundamentals of Photonic Crystal Guiding, Cambridge University Press, New York, 2009.
[8]	I. A. Sukhovanov, and I. V. Guryev, Photonic Crystals Physics and Practical Modeling, Springer Series in Optical Science, New York, 2009.
[9]	R. Gonalo, P. D. Maagt, M. Sorrolo, "Enhanced Patch antenna perfomnce by suppressing surface waves using PBG substrates,," IEEE transactions on microwave theory and techniques. Vol. 47, No. 11, pp. 2131-2138, November 1999.
[10]	E. Yablonovitch, T.J. Gmitter, "Photonic band structure: The face centered cubic case employing nonspherical atoms,” J. Physical review letters, Vol.67, N° 17, pp. 2295– 2298, 1991.
[11]	K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a Photonic Gap in Periodic Dielectric Structures,"Phys Rev Lett, 1990 Dec 17, vol 65, N°25, pp 3152-3155.
[12]	Costas M. Soukoulis, "Photonic Band Gap Materials," Proceedings of the NATO Advanced Study Institute on Photonic Band Gap Materials, Elounda, Crete, Greece , June 18-30, 1995.
[13]	C. v. Mee, P. Contu, P. Pintus, "One-dimensional photonic crystal design", Journal of Quantitative Spectroscopy & Radiative Transfer, Vol. 111, pp. 214–225, 2010.
[14]	H. Tian, Y. Ji, C. Li, H. Liu, "Transmission properties of one-dimensional graded photonic crystals and enlargement of omnidirectional negligible transmission gap", Elsevier, Optics Communications Vol 275, N°1, pp 83–89, July 2007.
[15]	B. Gallas S. Fission, E. Charron, A. Brunet-Bruneau, R. Vuye and J. Revory, " Making an omnidirectional reflector", Appl. Opt. 40, 5056-5063, 2001.
[16]	K. M.Chen, A. W. Sparks, H. C. Luan, D. R. Lim, K. wada, and L. C. Kimerling, "SiO2/TiO2 omni-directional reflector and microcavity resonator via the sol-gel method," Appl. Phys. Lett., Vol. 75, pp. 3805-3807, 1999.
[17]	D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omni-directional reflection from a one-dimensional dielectric lattice," Appl. Phys. A:Mater. Sci. Process., Vol. 68, pp. 25–28, 1999.
[18]	D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "All dielectric one dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control, " J. Lightwave Tech., Vol. 17, pp.2018–2024, 1999.
[19]	F. Scotognella, "Four-material one dimensional photonic crystals," Elsevier, Optical Materials, Vol. 34, N° 9, July 2012, pp 1610–1613.
[20]	K. M. Leung, and Y. F. Liu, "Photon band structures: The plane wave method", Physical Review B, 41, pp. 10188-10190, 1990.
[21]	S. Şimşek, "A novel method for designing one dimensional photonic crystals with given bandgap characteristics," Elsevier, Int. J. Electron. Commun. (AEÜ), Vol. 67, pp827– 832, 2013.
[22]	L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke and R. C. McPhedran, "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. Part I: Theory," Phys. Rev. E, Vol. 70, 056606, 2004.
[23]	L. C. Botten, N. A. Nicorovici, R. C. McPhedran, A. A. Asatryan, and C. M. de Sterke, “Photonic band structure calculations using scattering matrices'', Phys. Rev. E, Vol. 64, 046603, pp. 1-20, 2001.
[24]	J. B. Pendry, A. Mackinnon, "Calculation of photon dispersion, "Phys. Rev. Lett., 69, (3), pp. 2772–2775, 1992.

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Ouarda Barkat. (2015). Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. Journal of Electrical and Electronic Engineering, 3(2), 12-18. https://doi.org/10.11648/j.jeee.20150302.11

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ACS Style

Ouarda Barkat. Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. J. Electr. Electron. Eng. 2015, 3(2), 12-18. doi: 10.11648/j.jeee.20150302.11

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AMA Style

Ouarda Barkat. Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. J Electr Electron Eng. 2015;3(2):12-18. doi: 10.11648/j.jeee.20150302.11

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@article{10.11648/j.jeee.20150302.11,
  author = {Ouarda Barkat},
  title = {Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal},
  journal = {Journal of Electrical and Electronic Engineering},
  volume = {3},
  number = {2},
  pages = {12-18},
  doi = {10.11648/j.jeee.20150302.11},
  url = {https://doi.org/10.11648/j.jeee.20150302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20150302.11},
  abstract = {In this work, we demonstrate via numerical simulation the general design for one dimensional photonic crystal (1D- PC). In the design procedure, the transfer matrix method and Bloch theorem are used to determine the transmission coefficient and dispersion relation of (1D- PC) structure for both TE (transverse electric) and TM (transverse magnetic) modes. Results obtained showing the effect of the filling factor as well as the incident angle on the photonic band gap width. The analysis is carried out using MATLAB software tool. The accuracy of the analysis is tested by comparing the computed results with measurements published data.},
 year = {2015}
}

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TY  - JOUR
T1  - Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal
AU  - Ouarda Barkat
Y1  - 2015/03/10
PY  - 2015
N1  - https://doi.org/10.11648/j.jeee.20150302.11
DO  - 10.11648/j.jeee.20150302.11
T2  - Journal of Electrical and Electronic Engineering
JF  - Journal of Electrical and Electronic Engineering
JO  - Journal of Electrical and Electronic Engineering
SP  - 12
EP  - 18
PB  - Science Publishing Group
SN  - 2329-1605
UR  - https://doi.org/10.11648/j.jeee.20150302.11
AB  - In this work, we demonstrate via numerical simulation the general design for one dimensional photonic crystal (1D- PC). In the design procedure, the transfer matrix method and Bloch theorem are used to determine the transmission coefficient and dispersion relation of (1D- PC) structure for both TE (transverse electric) and TM (transverse magnetic) modes. Results obtained showing the effect of the filling factor as well as the incident angle on the photonic band gap width. The analysis is carried out using MATLAB software tool. The accuracy of the analysis is tested by comparing the computed results with measurements published data.
VL  - 3
IS  - 2
ER  -

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Author Information

Ouarda Barkat

Department of Electronics, University of Constantine 1, Constantine, Algeria

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APA Style

Ouarda Barkat. (2015). Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. Journal of Electrical and Electronic Engineering, 3(2), 12-18. https://doi.org/10.11648/j.jeee.20150302.11

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ACS Style

Ouarda Barkat. Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. J. Electr. Electron. Eng. 2015, 3(2), 12-18. doi: 10.11648/j.jeee.20150302.11

Copy | Download

AMA Style

Ouarda Barkat. Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal. J Electr Electron Eng. 2015;3(2):12-18. doi: 10.11648/j.jeee.20150302.11

Copy | Download

@article{10.11648/j.jeee.20150302.11,
  author = {Ouarda Barkat},
  title = {Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal},
  journal = {Journal of Electrical and Electronic Engineering},
  volume = {3},
  number = {2},
  pages = {12-18},
  doi = {10.11648/j.jeee.20150302.11},
  url = {https://doi.org/10.11648/j.jeee.20150302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20150302.11},
  abstract = {In this work, we demonstrate via numerical simulation the general design for one dimensional photonic crystal (1D- PC). In the design procedure, the transfer matrix method and Bloch theorem are used to determine the transmission coefficient and dispersion relation of (1D- PC) structure for both TE (transverse electric) and TM (transverse magnetic) modes. Results obtained showing the effect of the filling factor as well as the incident angle on the photonic band gap width. The analysis is carried out using MATLAB software tool. The accuracy of the analysis is tested by comparing the computed results with measurements published data.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Theoretical Investigation of Transmission and Dispersion Properties of One Dimensional Photonic Crystal
AU  - Ouarda Barkat
Y1  - 2015/03/10
PY  - 2015
N1  - https://doi.org/10.11648/j.jeee.20150302.11
DO  - 10.11648/j.jeee.20150302.11
T2  - Journal of Electrical and Electronic Engineering
JF  - Journal of Electrical and Electronic Engineering
JO  - Journal of Electrical and Electronic Engineering
SP  - 12
EP  - 18
PB  - Science Publishing Group
SN  - 2329-1605
UR  - https://doi.org/10.11648/j.jeee.20150302.11
AB  - In this work, we demonstrate via numerical simulation the general design for one dimensional photonic crystal (1D- PC). In the design procedure, the transfer matrix method and Bloch theorem are used to determine the transmission coefficient and dispersion relation of (1D- PC) structure for both TE (transverse electric) and TM (transverse magnetic) modes. Results obtained showing the effect of the filling factor as well as the incident angle on the photonic band gap width. The analysis is carried out using MATLAB software tool. The accuracy of the analysis is tested by comparing the computed results with measurements published data.
VL  - 3
IS  - 2
ER  -

Copy | Download