volume | PIER Journals

Abstract

Generalized band structure equation for photonic crystals which containing dielectric rods in metals medium was derived by using the plane wave expansion method. From the band structure, we can study band gap of photonic crystals in both E and H polarizations. Since metals are frequency-dependant materials, modification needs to be done on the plane wave expansion equation to calculate the metallic photonic crystals containing dielectric constant rods. To ease the calculation, simple Drude model for metals are used. In this model, the equation is without damping constant. We have plotted the band structure for photonic crystals in metals medium. Then, we studied the ffective plasma frequency of the structure from the band graph in E polarization mode (TM). We found that effective plasma frequency can be tailored as we want. Detailed results are presented with different sizes of radius. Comparison is made for different background materials.

1. Parui, S. K. and S. Das, "A simple electromagnetic bandgap structure for microstrip line," Proceedings of the IEEE First India Annual Conference, INDICON, 2004. Google Scholar

2. Chutinan, A., N. P. Kherani, and S. Zukotynski, "High-efficiency photonic crystal solar cell architecture," Optics Express, Vol. 17, 8, 2009.
doi:10.1364/OE.17.008871 Google Scholar

3. Haase, C. and H. Stiebig, "Light trapping in thin-film silicon solar cells with periodic structures," Conference Record of the 2006 IEEE 4th World Conference on Photovoltaic Energy Conversion, Hawaii, 1509-1512, 2006.

4. Guenneu, S., A. Nicolet, F. Zolla, and S. Lasquellec, "Numerical and theoretical study of photonic crystal fibers," Progress In Electromagnetics Research, Vol. 41, 271-305, 2003. Google Scholar

5. Nozhat, N. and N. Granpayeh, "Specialty fibers designed by photonic crystals," Progress In Electromagnetics Research, Vol. 99, 225-244, 2009.
doi:10.2528/PIER09092309 Google Scholar

6. Ozbay, E., B. Temelkuran, and M. Bayindir, "Microwave applications of photonic crystals," Progress In Electromagnetics Research, Vol. 41, 185-209, 2003.
doi:10.2528/PIER02010808 Google Scholar

7. Kuzmiak, V. and A. A. Maradudin, "Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components," Physical Review B, Vol. 58, 22, 1998.
doi:10.1103/PhysRevB.58.7230 Google Scholar

8. Pendry, J. B., "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, Vol. 76, 4, 1996.
doi:10.1103/PhysRevLett.76.4773 Google Scholar

9. Brand, S., R. A. Abram, and M. A. Kaliteevski, "Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods," Physical Review B, Vol. 75, 7, 2007.
doi:10.1103/PhysRevB.75.035102 Google Scholar

10. Hermann, D., M. Frank, K. Busch, and P. Wolfle, "Photonic band structure computations," Optics Express, Vol. 8, Jan. 29, 2001. Google Scholar

11. Plihal, M. and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Physical Review B, Vol. 44, 7, 1991.
doi:10.1103/PhysRevB.44.8565 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, 10, 1994.
doi:10.1103/PhysRevB.50.16835 Google Scholar

13. Zhou, Y.-S., B.-Y. Gu, and F.-H. Wang, "Photonic band gap structures and guide modes in two-dimensional magnetic photonic crystal heterostructures," European Physics Journal B, Vol. 37, 7, 2004. Google Scholar

14. Guo, S. and S. Albin, "Simple plane wave implementation for photonic crystal calculations," Optics Express, Vol. 11, 9, Jan. 27, 2003. Google Scholar

15. Rambabu, K., M. Mokhtaari, and J. Borneman, "Simplified computation of electromagnetic band-gap properties of via-holed metal patches," IEEE International Symposium on Electromagnetic Compatibility, EMC, 2007. Google Scholar

16. Qi, L.-M. and Z. Yang, "Modified plane wave method analysis of dielectric plasma photonic crystal," Progress In Electromagnetics Research, Vol. 91, 319-332, 2009.
doi:10.2528/PIER09022605 Google Scholar

17. Low, K. L., M. Z. M. Jafri, and S. A. Khan, "Band gap study using plane wave expansion method for metallic slab with air rods in E polarizing mode," Chinese Journal of Physics, Vol. 47, 10, 2009. Google Scholar

18. Xu, X., Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, "Effective plasma frequency in one-dimensional metallic-dieletric photonic crystals," Applied Physics Letters, Vol. 86, 3, 2005. Google Scholar

19. Kuzmiak, V. and A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Physical Review B, Vol. 55, 18, 1997. Google Scholar

20. Sakoda, K., Optical Properties of Photonic Crystals, 2005.

Dr. Khee Lam Low

Dr. Mohd Zubir Mat Jafri

Dr. Sohail A. Khan