Germanium Based Two-Dimensional Photonic Crystals with Square Lattice

Fairuz Aniqa Salwa; Muhammad Mominur Rahman; Muhammad Obaidur Rahman; Muhammad Abdul Mannan Chowdhury

doi:doi:10.11648/j.ajop.20190701.12

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Germanium Based Two-Dimensional Photonic Crystals with Square Lattice

Fairuz Aniqa Salwa, Muhammad Mominur Rahman, Muhammad Obaidur Rahman, Muhammad Abdul Mannan Chowdhury

Published in American Journal of Optics and Photonics (Volume 7, Issue 1)

Received: 11 March 2019 Accepted: 26 April 2019 Published: 15 May 2019

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Abstract

Using the plane-wave expansion method, we study the polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), surface plots, gap maps etc. of the two-dimensional photonic crystals with square lattice of germanium rods in air and vice versa. The obtained graphs for the two possible combinations are presented in this paper. All the results depict clear photonic band gaps. We describe the conditions for the largest TE and TM band gaps too. The square lattice of Ge rods in air offers a large TE photonic band gap of 48.02% (for rod radius of r = 0.2μm). Then we localize the TE mode by introducing a point defect and a line defect in the crystal. The point defect act as a resonator and the line defect act as a waveguide. The finite-difference time-domain analysis of the localized defect modes is presented also.

Published in	American Journal of Optics and Photonics (Volume 7, Issue 1)
DOI	10.11648/j.ajop.20190701.12
Page(s)	10-17
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 Crystals, Transverse Electric Modes, Transverse Magnetic Modes, Plane Wave Expansion Method, Finite Difference Time Domain Method, Photonic Band Diagram, Gap Map, Square Lattice

References

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[7]	I. A. Sukhoivanov and I. V. Guryev, Photonic Crystals Physics and Practical Modeling (Springer, 2005).
[8]	M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge, 2008).
[9]	J. D. Joannopoulos, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light, 1st ed. (Princeton University Press, 1995).
[10]	S. McCall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett., vol. 67, no. 15, pp. 2017–2020, Oct. 1991.
[11]	A. Taflove, S. C. Hagness, and K. S. Yee, Computationai Electrodynamics: The Finite-Difference Time-Domain Method, vol. 14, no. 3. 1966.
[12]	D. J. Griffiths, Introduction to Electrodynamics, Third edit. Prentice-Hall, 1999.
[13]	S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A, vol. 21, no. 9, p. 1769, 2004.
[14]	R. Antos and M. Veis, “Fourier Factorization in the Plane Wave Expansion Method in Modeling Photonic Crystals,” in Photonic Crystals - Introduction, Applications and Theory, no. 1, 2012, pp. 319–344.
[15]	C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics Nanostructures - Fundam. Appl., vol. 1, no. 1, pp. 1–13, 2003.
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[17]	Salwa, F. A., Rahman, M. M., Rahman, M. O. and Chowdhury, M. A. M. (2019) Germanium Based Two-Dimensional Photonic Crystals: The Hexagonal and Honeycomb Lattices. Optics and Photonics Journal, 9, 25-36. https://doi.org/10.4236/opj.2019.93004.
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APA Style

Fairuz Aniqa Salwa, Muhammad Mominur Rahman, Muhammad Obaidur Rahman, Muhammad Abdul Mannan Chowdhury. (2019). Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. American Journal of Optics and Photonics, 7(1), 10-17. https://doi.org/10.11648/j.ajop.20190701.12

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ACS Style

Fairuz Aniqa Salwa; Muhammad Mominur Rahman; Muhammad Obaidur Rahman; Muhammad Abdul Mannan Chowdhury. Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. Am. J. Opt. Photonics 2019, 7(1), 10-17. doi: 10.11648/j.ajop.20190701.12

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AMA Style

Fairuz Aniqa Salwa, Muhammad Mominur Rahman, Muhammad Obaidur Rahman, Muhammad Abdul Mannan Chowdhury. Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. Am J Opt Photonics. 2019;7(1):10-17. doi: 10.11648/j.ajop.20190701.12

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@article{10.11648/j.ajop.20190701.12,
  author = {Fairuz Aniqa Salwa and Muhammad Mominur Rahman and Muhammad Obaidur Rahman and Muhammad Abdul Mannan Chowdhury},
  title = {Germanium Based Two-Dimensional Photonic Crystals with Square Lattice},
  journal = {American Journal of Optics and Photonics},
  volume = {7},
  number = {1},
  pages = {10-17},
  doi = {10.11648/j.ajop.20190701.12},
  url = {https://doi.org/10.11648/j.ajop.20190701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20190701.12},
  abstract = {Using the plane-wave expansion method, we study the polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), surface plots, gap maps etc. of the two-dimensional photonic crystals with square lattice of germanium rods in air and vice versa. The obtained graphs for the two possible combinations are presented in this paper. All the results depict clear photonic band gaps. We describe the conditions for the largest TE and TM band gaps too. The square lattice of Ge rods in air offers a large TE photonic band gap of 48.02% (for rod radius of r = 0.2μm). Then we localize the TE mode by introducing a point defect and a line defect in the crystal. The point defect act as a resonator and the line defect act as a waveguide. The finite-difference time-domain analysis of the localized defect modes is presented also.},
 year = {2019}
}

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TY  - JOUR
T1  - Germanium Based Two-Dimensional Photonic Crystals with Square Lattice
AU  - Fairuz Aniqa Salwa
AU  - Muhammad Mominur Rahman
AU  - Muhammad Obaidur Rahman
AU  - Muhammad Abdul Mannan Chowdhury
Y1  - 2019/05/15
PY  - 2019
N1  - https://doi.org/10.11648/j.ajop.20190701.12
DO  - 10.11648/j.ajop.20190701.12
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
SP  - 10
EP  - 17
PB  - Science Publishing Group
SN  - 2330-8494
UR  - https://doi.org/10.11648/j.ajop.20190701.12
AB  - Using the plane-wave expansion method, we study the polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), surface plots, gap maps etc. of the two-dimensional photonic crystals with square lattice of germanium rods in air and vice versa. The obtained graphs for the two possible combinations are presented in this paper. All the results depict clear photonic band gaps. We describe the conditions for the largest TE and TM band gaps too. The square lattice of Ge rods in air offers a large TE photonic band gap of 48.02% (for rod radius of r = 0.2μm). Then we localize the TE mode by introducing a point defect and a line defect in the crystal. The point defect act as a resonator and the line defect act as a waveguide. The finite-difference time-domain analysis of the localized defect modes is presented also.
VL  - 7
IS  - 1
ER  -

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Author Information

Fairuz Aniqa Salwa

Department of Physics, Jahangirnagar University, Savar, Dhaka, Bangladesh
Muhammad Mominur Rahman

Department of Physics, Jahangirnagar University, Savar, Dhaka, Bangladesh
Muhammad Obaidur Rahman

Department of Physics, Jahangirnagar University, Savar, Dhaka, Bangladesh
Muhammad Abdul Mannan Chowdhury

Department of Physics, Jahangirnagar University, Savar, Dhaka, Bangladesh

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Plain Text BibTeX RIS

APA Style

Fairuz Aniqa Salwa, Muhammad Mominur Rahman, Muhammad Obaidur Rahman, Muhammad Abdul Mannan Chowdhury. (2019). Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. American Journal of Optics and Photonics, 7(1), 10-17. https://doi.org/10.11648/j.ajop.20190701.12

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ACS Style

Fairuz Aniqa Salwa; Muhammad Mominur Rahman; Muhammad Obaidur Rahman; Muhammad Abdul Mannan Chowdhury. Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. Am. J. Opt. Photonics 2019, 7(1), 10-17. doi: 10.11648/j.ajop.20190701.12

Copy | Download

AMA Style

Fairuz Aniqa Salwa, Muhammad Mominur Rahman, Muhammad Obaidur Rahman, Muhammad Abdul Mannan Chowdhury. Germanium Based Two-Dimensional Photonic Crystals with Square Lattice. Am J Opt Photonics. 2019;7(1):10-17. doi: 10.11648/j.ajop.20190701.12

Copy | Download

@article{10.11648/j.ajop.20190701.12,
  author = {Fairuz Aniqa Salwa and Muhammad Mominur Rahman and Muhammad Obaidur Rahman and Muhammad Abdul Mannan Chowdhury},
  title = {Germanium Based Two-Dimensional Photonic Crystals with Square Lattice},
  journal = {American Journal of Optics and Photonics},
  volume = {7},
  number = {1},
  pages = {10-17},
  doi = {10.11648/j.ajop.20190701.12},
  url = {https://doi.org/10.11648/j.ajop.20190701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20190701.12},
  abstract = {Using the plane-wave expansion method, we study the polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), surface plots, gap maps etc. of the two-dimensional photonic crystals with square lattice of germanium rods in air and vice versa. The obtained graphs for the two possible combinations are presented in this paper. All the results depict clear photonic band gaps. We describe the conditions for the largest TE and TM band gaps too. The square lattice of Ge rods in air offers a large TE photonic band gap of 48.02% (for rod radius of r = 0.2μm). Then we localize the TE mode by introducing a point defect and a line defect in the crystal. The point defect act as a resonator and the line defect act as a waveguide. The finite-difference time-domain analysis of the localized defect modes is presented also.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Germanium Based Two-Dimensional Photonic Crystals with Square Lattice
AU  - Fairuz Aniqa Salwa
AU  - Muhammad Mominur Rahman
AU  - Muhammad Obaidur Rahman
AU  - Muhammad Abdul Mannan Chowdhury
Y1  - 2019/05/15
PY  - 2019
N1  - https://doi.org/10.11648/j.ajop.20190701.12
DO  - 10.11648/j.ajop.20190701.12
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
SP  - 10
EP  - 17
PB  - Science Publishing Group
SN  - 2330-8494
UR  - https://doi.org/10.11648/j.ajop.20190701.12
AB  - Using the plane-wave expansion method, we study the polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), surface plots, gap maps etc. of the two-dimensional photonic crystals with square lattice of germanium rods in air and vice versa. The obtained graphs for the two possible combinations are presented in this paper. All the results depict clear photonic band gaps. We describe the conditions for the largest TE and TM band gaps too. The square lattice of Ge rods in air offers a large TE photonic band gap of 48.02% (for rod radius of r = 0.2μm). Then we localize the TE mode by introducing a point defect and a line defect in the crystal. The point defect act as a resonator and the line defect act as a waveguide. The finite-difference time-domain analysis of the localized defect modes is presented also.
VL  - 7
IS  - 1
ER  -

Copy | Download