Periodic and quasi-periodic Cantor-like bandgap structures that bordered upon a medium of refractive index n_(0) are analyzed. An immersion model is used with the assumption that each layer is embedded between two identical regions of refractive index n_(0) and thickness d_(0), where d_(0) is set equal to zero. Transmittance and group velocity are determined. Their dependence on n_(0) is emphasized. Relations for the midgap value of the normalized group velocity are given. By use of these relations, diagrams are completed at different values of n_(0), showing the pairs of quarter-wave-layer refractive indices at which there is an apparent superluminal tunneling through the finite periodic and quasi-periodic Cantor-like bandgap structures.
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