Document Type : Original Article
Authors
Department of Photonics, Laser and Optical Engineering, University of Bonab, Bonab, Iran
Abstract
In this paper, surface polaritons (SPs) at the interface of a semi-infinite homogeneous dielectric medium and a one-dimensional photonic crystal (PC) have been investigated theoretically. The PC is made of the alternate layers of an isotropic ordinary dielectric and a graphene-based hyperbolic metamaterial layers. The effective medium approach has been used for the study of the metamaterial layers and it is shown that they have hyperbolic dispersion in a certain frequency range at THz region. The obtained results show that the structure has some photonic band gaps in the hyperbolic and elliptical frequency regions for both TE and TM polarizations and can support the SPs in these frequency ranges. It is observed that the characteristics of the SPs depend on the geometrical parameters of the structure and optical parameters of the graphene monolayers. In the following, the electromagnetic field profiles of some SPs have been plotted and it is shown that the modes of the first band gap are more localized than the modes of the second band gap. Finally, the intensity distribution of a TM-polarized Gaussian beam inside and outside the PC has been simulated which is verifying the localization of the SPs at the interface of the structure.
Keywords
- J Nkoma, R Loudon, and D R Tilley, J. Phys. C: Solid State Phys. 7 (1977) 3547.
- S A Maier, “Plasmonics: “Fundamentals” and Applications”, Springer, Germany (2007) .
- V M Agranovich and D L Mills, “Surface Polaritons-Electromagnetic Waves at Surfaces and Interfaces”, Elsevier Science Ltd., Netherlands (1982) .
- P Yeh, A Yariv, and C Hong, J. Opt. Soc. Am. 67 (1977) 423.
- P Yeh, P Chen, and A Yariv, Appl. Phys. Lett. 32 (1978) 370.
- G Margheri, T Del Rosso, S Sottini, S Trigari, and E Giorgetti, Opt. Express16 (2008) 9869.
- J Martínez, A Ródenas, M Aguiló, T Fernandez, J Solis, and F Díaz, Opt. Lett. 41 (2016) 2493.
- Y Zong, P Lang, L Yu, G Duan, and Z Pan, IEEE Photonic Tech L. 29 (2017) 466.
7. S Dhara, C Y Lu, P Magudapathy, Y F Huang, W S Tu, and K H Chen, Appl. Phys. Lett. 106 (2015) 023101.
10. J Gaspar-Armenta and F Villa, J. Opt. Soc. Am. B, 20 (2003) 2349.
11. J Martorell, D Sprung, and G Morozov, J. Opt. A: Pure Appl. Opt. 8 (2006) 630.
12. [12] J. Gaspar-Armenta, F. Villa, T. López-Rios, Opt. Commun. 216 (2003) 379.
13. I V Soboleva, E Descrovi, C Summonte, A A Fedyanin, and F Giorgis, Appl. Phys. Lett. 94 (2009) 231122.
14. M Shinn and W Robertson, Sensors and Actuators B, 105 (2005) 360.
15. Y Wan, Z Zheng, W Kong, X Zhao, Y Liu, Y Bian, and J. Liu, Opt. Express, 20 (2012) 8998.
16. D Soto-Puebla, M Xiao, and F Ramos-Mendieta, Phys. Lett. A 326 (2004) 273.
17. D Bria, B Djafari-Rouhani, A Akjouj, L Dobrzynski, J P Vigneron, E H El Boudouti, and A Nougaoui, Phys. Rev. E 69 (2004) 066613.
18. S Feng, J Merle Elson, and P L Overfelt, Opt. Express13 (2005) 4113.
19. A Madani and S Roshan Entezar, Physica B 431 (2013) 1.
20. S Roshan Entezar, Z Saleki, A Madani, Physica B 478 (2015) 122.
21. Z Saleki, S Roshan Entezar, and A Madani, Appl. Opt. 56 (2017) 317.
22. A Namdar, Opt. Commun. 278 (2007) 194.
23. S Roshan Entezar, A Madani, A Namdar, and H Tajalli, J. Magn. Magn. Mater. 324 (2012) 1739.
24. A Madani and S Roshan Entezar, Superlattices and Microstructures 75 (2014) 692.
25. A Poddubny, I Iorsh, P Belov, and Y Kivshar, Nat. Photonics 7 (2013) 948.
26. V Drachev, V A Podolskiy, and A V Kildishev, Opt. Express 21 (2013) 15048.
27. Y Li, J Zhang, S Qu, J Wang, Y Pang, Z Xu and A Zhang, J. Phys. D: Appl. Phys. 48 (2015) 335101.
28. C Lv, W Li, X Jiang, and J Cao, EPL 105 (2014) 28003.
29. X Li, Z Liang, X Liu, X Jiang, and J Zi, Appl. Phys. Lett. 93 (2008) 171111.
30. J Yang, X Hu, X Li, Z Liu, X Jiang, and J Zi, Opt. Lett. 35 (2010) 16.
31. Y Chang, C Liu, C Liu, S Zhang, S R Marder, E E Narimanov, Z Zhong, and T B Norris, Nat. Commun. 7 (2016) 10568.
32. K S Novoselov, A K Geim, S V Morozov, D Jiang, Y Zhang, S V Dubonos, I V Grigorieva, and A A Firsov, Science 306 (2004) 666.
33. A K Geim, Science, 324 (2009) 1530.
34. A Madani and S Roshan Entezar, Photonics and Nanostructures-Fundamentals and Applications 25 (2017) 58.
35. G W Hanson, J. Appl. Phys. 104 (2008) 084314.
I Iorsh, I Mukhin, I Shadrivov, P Belov, and Y Kivshar, Phys. Rev. B 87 (2013) 075416.
)