Prospects of fractal filters and reflectors

The authors study the transmission and reflection properties of multilayered slab made from two kinds of dielectrics. The relative permittivity between them is assumed to be a complex number. The pattern of the slab follows the N^th stage of the Cantor fractal set construction. For easy fabrication of the slabs, the values of N are restricted to 3,4 or, maximum, 5. Due to the self-similarity between the various parts of the considered device an exact solution yielding the transmission t and the reflection r coefficients at normal incidence is obtained. The results show that there exist zones of the waveband in which |t| is practically unity and others for which a total reflection is predicted. This suggests the possibility of designing filters and reflecting coating with almost ideal properties