The Study of Two Dimensional Photonic Crystal Made of Two Concentric Cylindrical Nano-layers of Dielectric with Negative Refraction Index

In this paper, we study the propagation of electromagnetic wave in 2D photonic crystal (PC) made of two concentric cylinders of dielectric with the negative refraction index for TM mode in two kind structures. Applying the boundary conditions in Maxwell equation in periodic structures, we change this equation to Helmholtz equation. By solving this equation in two dimensions and using plane wave expansion method (PWEM), we can find the band gaps and allowed modes. We consider two structures with two concentric cylindrical rods; the external rode in the first structure consists of negative refraction index material while in the second structure it is made of a dielectric material. It is shown that by increasing the diameter of the cylinder which is composed of negative refraction index material in both structures, we can obtain wider band gaps in compare to the structures which there is no negative refractive index materials.