volume | PIER Journals

Abstract

This work describes a theoretical study of filters using a defect in one-dimensional photonic comb-like structure. This photonic comb-like structure is constituted by finite or infinite segments which have negative permeability and grafted in each site by a finite number of lateral branches (play the role of the resonators), which consists of a negative permittivity. Numerical results exhibit the permissible bands which are separated by gaps (forbidden band). These gaps originate not only from the periodicity of the system but also from the resonance states of the grafted lateral branches. We study the effect of the presence of a resonator defect on the transmission behavior, phase, and phase time. The electromagnetic band structure shows that there is a defect mode in the gap. The transmission rate and the reduced frequency of this mode are related to the variation of defect length. Similarly, we calculate, for the first time, the quality factor evolution of this defect mode when the defect length varies. This structure can be used as a new optical filter in the microwave range with a high factor of quality and of transmission.

1. Zhou, H., C. Wang, and H. Peng, "A novel double-incidence and multi-band left-handed metamaterials composed of double Z-shaped structure," Journal of Materials Science: Materials in Electronics, Vol. 27, 2534-2544, 2016.

2. Bi, K., J. Zhou, X. Liu, C. Lan, and H. Zhao, "Multi-band negative refractive index in ferrite-based metamaterials," Progress In Electromagnetic Research, Vol. 140, 457-469, 2013.

3. Li, J., F.-Q. Yang, and J. F. Dong, "Design and simulation of L-shaped chiral negative refractive index structure," Progress In Electromagnetic Research, Vol. 116, 395-408, 2011.

4. Cao, T. and M. J. Cryan, "Modeling of optical trapping using double negative index fishnet metamaterials," Progress In Electromagnetic Research, Vol. 129, 33-49, 2012.

5. Zhu, W., I. D. Rukhlenko, and M. Premaratne, "Maneuvering propagation of surface plasmon polaritons using complementary medium inserts," IEEE Photonics Journal, Vol. 4, No. 3, 741-747, 2012.

6. Zhu, J. H., S. Y. Wei, N. Haldolaarachchige, J. He, D. P. Young, and Z. H. Guo, "Very large magnetoresistive graphene disk with negative permittivity," Nanoscale, Vol. 4, 152-156, 2012.

7. Cheng, Y., Y. Nie, and R. Z. Gong, "Giant optical activity and negative refractive index using complementary U-shaped structure assembly," Progress In Electromagnetic Research M, Vol. 25, 239-253, 2012.

8. Zeng, R., Y. Yang, and S. Zhu, "Casimir force between anisotropic single-negative metamaterials," Physical Review A, Vol. 87, 063823-063829, 2013.

9. Xu, H. X., G. M. Wang, M. Q. Qi, and H. Y. Zeng, "Ultra-small single-negative electric metamaterials for electromagnetic coupling reduction of microstrip antenna array," Optics Express, Vol. 20, 21968-21976, 2012.

10. Alu, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency," IEEE Transactions on Antennas and Propagation, Vol. 51, 2558-2571, 2003.

11. Dhouibi, A., S. N. Burokur, A. Lustrac, and A. Priou, "Comparison of compact electric-LC resonators for negative permittivity metamaterials," Microwave and Optical Technology Letters, Vol. 54, 2287-2295, 2012.

12. Sun, K., P. Xie, Z. Wang, T. Su, Q. Shao, J. Ryu, X. Zhang, J. Guo, A. Shankar, J. Li, R. Fan, D. Cao, and Z. Guo, "Flexible polydimethylsiloxane/multi-walled carbon nanotubes membranous metacomposites with negative permittivity," Polymer, Vol. 125, 50-57, 2017.

13. Naqui, J. and F. Martin, "Angular displacement and velocity sensors based on electric-LC (ELC) loaded microstrip lines," IEEE Sensors Journal, Vol. 14, No. 4, 939-940, 2014.

14. Rawat, V., V. Nadkarni, and S. N. Kale, "Band flex fuel sensor using electrical metamaterialdevice," Applied Physics A, Vol. 123, 75-78, 2017.

15. Khan, O. M., Z. U. Islam, Q. U. Islam, and F. A. Bhatti, "Multiband high-gain printed yagi array using square spiral ring metamaterial structures for S-band applications," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 1100-1103, 2014.

16. Xu, X., Y. Li, and X. Miao, "Robust waveguide against surface perturbations due to band inversion in two kinds of single-negative metamaterials," Europhysics Letters, Vol. 116, 44001-44007, 2016.

17. Jiang, H., H. Chen, and Y. E. Zhang, "Properties of one-dimensional photonic crystals containing single-negative materials," Physics Letters E, Vol. 69, 066607-066612, 2004.

18. Wang, L.-G., H. Chen, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials," Physical Review B, Vol. 70, 245102-245107, 2004.

19. Mackay, T. G., "Towards metamaterials with giant dielectric anisotropy via homogenization: An analytical study," Photonics and Nanostructures — Fundamentals and Applications, Vol. 13, 8-19, 2015.

20. Mikhaylovskiy, R. V., E. Hendry, and V. V. Kruglyak, "Negative permeability due to exchange spin-wave resonances in thin magnetic films with surface pinning," Physical Review, Vol. 82, 195446-195455, 2010.

21. Thibaudau, P. and J. Tranchida, "Frequency-dependent effective permeability tensor of unsaturated polycrystalline ferrites," Journal of Physics: Applied Physics, Vol. 118, 053901-053901, 2015.

22. Thapaa, K. B., P. C. Pandey, P. P. Singhc, and S. P. Ojha, "Tunable characteristics of one dimensional magnetic photonic crystal composed with single-negative materials," Optik, Vol. 124, 6631-6635, 2013.

23. Marathe, D. and K. Kulat, "A compact triple-band negative permittivity metamaterial for C, X-band applications," International Journal of Antennas and Propagation, Vol. 2017, 1-13, 2017.

24. Faruque, I. S. S., M. R. Iqbal, and M. T. Islam, "A New SNG metamaterial for S-band microwave applications," Journal of Electrical & Electronics Engineering, Vol. 7, 13-16, 2014.

25. Vasseur, J. O., P. A. Deymier, L. Dolorzynski, B. Djafari-Rouhani, and A. Akjouj, "Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures," Physical Review B, Vol. 55, 10434-10442, 1997.

26. Srivastava, S. K. and S. P. Ojha, "Enlarged photonic band gaps in one-dimensional magnetic star waveguide structure," Progress In Electromagnetic Research M, Vol. 9, 21-34, 2009.

27. Ben-Ali, Y., Z. Tahri, A. Ouariach, and D. Bria, "Double frequency filtering by photonic comblike," IEEE Xplore, 1-6, 2019.

28. Vasseur, J. O., P. A. Deymier, L. Dolorzynski, B. Djafari-Rouhani, and A. Akjouj, "Defect modes in one-dimensional comblike photonic waveguides," Physical Review B, 13446-13452, 1999.

29. Cocoletzi, G. H., L. Dobrzynski, B. Djafari-Rouhani, H. Al-Wahsh, and D. Bria, "Electromagnetic wave propagation in quasi-one-dimensional comb-like structures made up of dissipative negative-phase-velocity materials," Journal of Physics: Condensed Matter, Vol. 18, 3683-3690, 2006.

30. Yin, C. P. and H. Z.Wang, "Narrow transmission bands of quasi-1D comb-like photonic waveguides containing negative index materials," Physics Letters A, Vol. 373, 1093-1096, 2009.

31. Weng, Y., Z. G. Wang, and H. Chen, "Band structure of comb-like photonic crystals containing meta-materials," Optics Communications, Vol. 277, 80-83, 2007.

32. Zhang, L., Z. Wang, H. Chen, H. Li, and Y. Zhang, "Experimental study of quasi-one-dimensional comb-like photonic crystals containing left-handed material," Optics Communications, Vol. 281, 3681-3685, 2008.

33. Tan, W., Y. Sun, Z. G. Wang, and H. Chen, "Propagation of photons in metallic chain through side-branch resonators," Journal of Physics D: Applied Physics, Vol. 44, 335101-335101, 2011.

34. Tan, W., Z. Wang, and H. Chen, "Complete tunning of light through mu-negative media," Progress In Electromagnetic Research M, Vol. 8, 27-37, 2009.

35. Ben-Ali, Y., Z. Tahri, F. Falyouni, and D. Bria, "Study about a filter using a resonator defect in a one-dimensional photonic comb containing a left-hand material," Proceedings of the 1st International Conference on Electronic Engineering and Renewable Energy, ICEERE, Saidia, 2018.

36. Fang, W., Y. Z. Cheng, X. Wang, Y. N. Zhang, Y. Nie, and R. Z. Gong, "Narrow band filter at 1550 nm based on quasi-one-dimensional photonic crystal with a mirror-symmetric heterostructure," Materials, Vol. 11, 1099-1108, 2018.

37. Wang, F., Y. Z. Cheng, X. Wang, D. Qi, H. Luo, and R. Z. Gong, "Effective modulation of the photonic band gap based on Ge/ZnSone dimensional photonic crystal at the infrared band," Optical Materials, Vol. 75, 373-378, 2018.

38. Vasseur, J. O., P. A. Deymier, L. Dolorzynski, B. Djafari-Rouhani, and A. Akjouj, "Defect modes in one-dimensional comblike photonic waveguides," Physical Review, Vol. 59, 13446-13452, 1999.

39. Ben-Ali, Y., Z. Tahri, A. Bouzidi, D. Bria, A. Khettabi, and A. Nougaoui, "Propagation of electromagnetic waves in a one-dimensional photonic crystal containing two defects," Journal of Materials and Environmental Sciences, Vol. 8, 870-876, 2017.

Professor Youssef Ben-Ali

Dr. Zakaria Tahri

Dr. Driss Bria