Abstract: The optical properties of a cantor-like metal-insulator superlattice for both p-polarized and s- polarized wave are studied by employing the transfer matrix formalism. Based on the hydrodynamic theory and taking account of retardation effect, we have calculated the dispersion relations of the electromagnetic modes of the superlattices. The results show that the dispersion relations of the modes have rich multi-fractal structure, and the frequency gaps, in which there are strong reflective peaks, appear strikingly in the region of the extreme ultraviolet and soft x-ray. Around the fixed points, the patterns of the bands are scale invariant.!9
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