Analytical solutions for the one-dimensional periodic structure consisting of left-handed medium

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  • 15 October 2002
Abstract
We present in this paper an analytical solution when both the permittivity and permeability are periodic in one dimensional (1D) case. With the analytical solution, we show that there will be complex solutions if the periodic structure includes the left-handed medium. The imaginary solutions corresponds to the evanescent waves supported by the photon tunnelling effect of the left-handed media under a certain of conditions. The band structure including both the normal real modes and the evanescent modes is specially interesting as we can see from a few specific situations in this letter. There is a region in which the imaginary wave vectors of the evanescent waves must lie in. Discrete solutions can also be obtained for the normal modes in the band structure.

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