Numerical relationship of Metallic Photonic Crystals' Effective Plasma Frequency with Relative Permittivity

Publication Issue: 
Volume 37, Issue 1, 2016
Page No: 
Date Received: 
Wednesday, August 24, 2016
Authors' Name: 
Low Khee Lam
Mohd Zubir Mat Jafri
Authors' Affiliation and Address: 
KDU Penang University College, Penang, 10400 Malaysia
Universiti Sains Malaysia, Penang, 11700 Malaysia
Several analytical models have been used to investigate the effective plasma frequency of photonic crystals involving metallic components. In recent studies, the analysis models were not suitable for revealing detailed band structure effects. Furthermore, the effect of the relative permittivity used in photonic crystals has not been discussed and related to the analytical model. By using the modified plane wave expansion method in the literature, we have plotted band structure graphs for photonic crystals containing metallic components and photonic crystals in metallic media. We investigated two metals: copper ( ωp =1914 THz) and aluminum ( ωp=3570 THz). We obtained theoretical values of the effective plasma frequency by varying the relative permittivity and filling fraction using band structure graphs. Then we obtained a numerical model of effective plasma frequency and relative permittivity using regression method for both copper and aluminum. Both shared the same equation. Next the derivation was expanded to photonic crystals in metallic media, going through the same process. A numerical model of effective plasma frequency and relative permittivity was obtained for photonic crystals in metallic media.