PhotonIcs and Electromagnetics Research Symposium,
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Published: 2015-07-09
Photonic Band Structure and Field Distribution for TE Polarization. High Plasmon Concentration in the Corners of Metallic Rods of a 2D Photonic Crystal
By
Danny Manuel Calvo Velasco,
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    Danny Manuel Calvo Velasco

    Universidad del Valle, Colombia

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Nelson Porras-Montenegro
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    Nelson Porras-Montenegro

    Universidad del Valle, Colombia

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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)73-77
Abstract
In this work we calculated the photonic band structure (PBS) of a square 2D photonic crystal (PC) made of square metallic rods embedded in air, considering a Drude type dielectric function without loss for different values of the rod plasma frequency, ωp . The PBS was calculated for TE polarization in the Γ-X direction using the revised plane wave method (RPWM), considering the Li’s rules for the product of two periodic functions. We found that the PBS presents flat bands below and above the surface plasmon frequency (SPF), and by means of the distribution of the square module of the magnetic component of the electromagnetic radiation, |Hz |2 , in the crystal unit cell, we found that these bands are related with the existence of plasmons in the surface of the rods, as it has been discussed and published in previous works. Besides these findings, we found a high concentration of the square module of the electric component of the electromagnetic radiation, |E|2 , close to the rod corners, which is a signature of the existence of localize surface plasmons, due to the geometry of the PCs structure. On the other hand, we found that |Hz |2 presents a distribution which does not change in passing from the metallic regime to the dielectric one for frequencies close to ωp , while |E|2 is distributed only inside the rods for frequencies below ωp , and essentially in the whole unit cell above this value.
Citation
Danny Manuel Calvo Velasco, and Nelson Porras-Montenegro, "Photonic Band Structure and Field Distribution for TE Polarization. High Plasmon Concentration in the Corners of Metallic Rods of a 2D Photonic Crystal," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)73-77
References

1. Joannopoulos, J. D., S. G. Johnson and J. N. Winn and R. D. Meade, Photonic Crystals: Molding the Flow of Light, Pricenton University Press, Pricenton, 2008.        Google Scholar

2. Sakoda, K., Optical Properties of Photonic Cristals, 2nd Edition Ed., Springer-Verlag, Berlin, Heidelberg, 2005.        Google Scholar

3. Ramakrishna, , S. A. and T. M. Grzegorczyk and Physics and Applications of Negative Refractive Index Materials and Taylos & Francis Group and Bellingham, S. A. and T. M. Grzegorczyk, 2009.        Google Scholar

4. Engheta, N. and R. W. Ziolkoshowski, Metamaterials: Physics and Engineering Explorations, IEEE Press, Wiley-Interscience, 2006.        Google Scholar

5. Cavalcanti, S. B., M. de Dios-Leyva, E. Reyes-Gómez, and L. E. Oliveira, "Band structure and band-gap control in photonic superlattices," Physical Review B, Vol. 74, No. 15, October 2006.
doi:10.1103/physrevb.74.153102        Google Scholar

6. González, Luz E. and N. Porras-Montenegro, "Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal," Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 4, 773–777, January 2012.
doi:10.1016/j.physe.2011.11.018        Google Scholar

7. Diaz-Valencia, B.F. and J.M. Calero, "Photonic band gaps of a two-dimensional square lattice composed by superconducting hollow rods," Physica C: Superconductivity and its Applications, Vol. 505, 74–79, October 2014.
doi:10.1016/j.physc.2014.07.012        Google Scholar

8. López, J., Luz E. González, M. F. Quiñonez, M. E. Gómez, N. Porras-Montenegro, and G. Zambrano, "Magnetic field role on the structure and optical response of photonic crystals based on ferrofluids containing Co0.25Zn0.75Fe2O4 nanoparticles," Journal of Applied Physics, Vol. 115, No. 19, May 2014.
doi:10.1063/1.4876315        Google Scholar

9. Sakoda, Kazuaki, "Electromagnetic eigenmodes of a three-dimensional photonic fractal," Physical Review B, Vol. 72, No. 18, November 2005.
doi:10.1103/physrevb.72.184201        Google Scholar

10. Mejía-Salazar, J. R., N. Porras-Montenegro, E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira, "Plasmon polaritons in 1D Cantor-like fractal photonic superlattices containing a left-handed material," EPL (Europhysics Letters), Vol. 95, No. 2, 24004, July 2011.
doi:10.1209/0295-5075/95/24004        Google Scholar

11. Veselago, V., L. Braginsky and V. Shklover and C. Hafner, ""Negative refractive index materials," J. Comput. Theor. Nanosci., Vol. 3, 1, 2006.        Google Scholar

12. Kuzmiak, V., A. A. Maradudin, and F. Pincemin, "Photonic band structures of two-dimensional systems containing metallic components," Physical Review B, Vol. 50, No. 23, 16835–16844, December 1994.
doi:10.1103/physrevb.50.16835        Google Scholar

13. Sakoda, Kazuaki, Noriko Kawai, Takunori Ito, Alongkarn Chutinan, Susumu Noda, Tsuneo Mitsuyu, and Kazuyuki Hirao, "Photonic bands of metallic systems. I. Principle of calculation and accuracy," Physical Review B, Vol. 64, No. 4, July 2001.
doi:10.1103/physrevb.64.045116        Google Scholar

14. Huang, Kerwyn Casey, Peter Bienstman, John. D. Joannopoulos, Keith A. Nelson, and Shanhui Fan, "Phonon-polariton excitations in photonic crystals," Physical Review B, Vol. 68, No. 7, August 2003.
doi:10.1103/physrevb.68.075209        Google Scholar

15. Maier, S., Plasmonics: Fundamentals and Applications, Springer Science+Business Media LLC, 2007.        Google Scholar

16. Ito, Takunori and Kazuaki Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Physical Review B, Vol. 64, No. 4, July 2001.
doi:10.1103/physrevb.64.045117        Google Scholar

17. Moreno, Esteban, Daniel Erni, and Christian Hafner, "Band structure computations of metallic photonic crystals with the multiple multipole method," Physical Review B, Vol. 65, No. 15, April 2002.
doi:10.1103/physrevb.65.155120        Google Scholar

18. Shi, Shouyuan, Caihua Chen, and Dennis W. Prather, "Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs," Applied Physics Letters, Vol. 86, No. 4, 043104, January 2005.
doi:10.1063/1.1855425        Google Scholar

19. Li, Lifeng, "Use of Fourier series in the analysis of discontinuous periodic structures," Journal of the Optical Society of America A, Vol. 13, No. 9, 1870, September 1996.
doi:10.1364/josaa.13.001870        Google Scholar

20. Lalanne, Philippe, "Effective properties and band structures of lamellar subwavelength crystals: Plane-wave method revisited," Physical Review B, Vol. 58, No. 15, 9801–9807, October 1998.
doi:10.1103/physrevb.58.9801        Google Scholar

21. Kitell, C., Introduction to Solid States Physics, 7th Edition Ed., Wiley, New York, 1966.        Google Scholar

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