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.
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
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.
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
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
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
8. Pendry, J. B., "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, Vol. 76, 4, 1996. doi:10.1103/PhysRevLett.76.4773
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
10. Hermann, D., M. Frank, K. Busch, and P. Wolfle, "Photonic band structure computations," Optics Express, Vol. 8, Jan. 29, 2001.
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
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
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.
14. Guo, S. and S. Albin, "Simple plane wave implementation for photonic crystal calculations," Optics Express, Vol. 11, 9, Jan. 27, 2003.
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.
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
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.
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.
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.
20. Sakoda, K., Optical Properties of Photonic Crystals, 2005.