Abstract
By using plane wave expansion method, we calculated the photonic band structure of metal cylinders in a dielectric medium. The photonic crystal is an identical, symmetrical structure with an infinite array of metallic rods. Arrangement of the metallic rods used is square lattice. The dielectric function of the metal from which the cylinders are formed has a simple, free electron form e(ω)=1-(ωp 2 /ω 2 ) where ωp is the plasma frequency of the conducting electron. We manage to show the band structure of the square lattice. We found the relation between the band gap size and the filling fraction for some widely used material. For an example, FR-4, silicon, resin, teflon etc. The relation between the band gap size and the dielectric constant of the medium was studied.
Highlights
Mathematical formulationThe periodic structure is assumed along the x axis
In this study, we focused on generalizing the equation from PWE method for calculating the band structure
S(x)=1 if x|| is inside the cross section of the cylinder centered at the origin of coordinates and S(x)=0 if x|| outside this cross section. ε0 is the dielectric constant of the medium and ε(ω) is the free electron dielectric function for metallic cylinders
Summary
The periodic structure is assumed along the x axis. Where G|| is a vector of the lattice reciprocal and Fourier coefficients of the (G|| ) showed as below (G|| )
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