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Tunable transmission and defect mode in one-dimensional ternary left-handed photonic crystal

We study the transmission of a one-dimensional ternary left-handed photonic crystal which is consisting of three alternating slabs in the form of {ABC}, where A and C represent two kinds of positive- refractive-index materials, and B represents the negative-refractive-index material. Firstly, we obtain the dispersion equation based on the boundary conditions and Bloch theorem. By construing the obtained dispersion relation theoretically we demonstrated that a zero averaged refractive index (ZARI) gap which is around the frequency where the average refractive index vanishes appears. Secondly, we investigate the dependence of the transmission on the thickness of slabs by changing the thickness of slab A, B and C respectively. We find that the transmission of such a structure can be made tunable. This novel property may be very useful in designing tunable filters because the position of band gaps in such a structure can be chosen expediently. Furthermore, we study the property of defect mode of such a structure, and find that the defect mode doesn't always appear simultaneously in both Bragg and ZARI gaps of the transmission spectrum. It can be selected to appear either in the Bragg gap or in the ZARI gap.