Transverse Electromagnetic Modes of Menger Sponge

In this article, an analytical solution for the electromagnetic modes of a Menger sponge using field equations of fractional space is presented. In order to realize the electromagnetic modes in non-integer dimension space, the fields inside the Menger sponge are expressed using a fractional parameter 2 ≤ D ≤ 3. The modes are calculated under two conditions of boundaries i.e., PMC and PEC, for D = 3 correspond to ordinary integer dimension space. Generalized solution for lossless and source free medium is studied for non-integer dimension. As anticipated, the dimension of media have effect on electric and magnetic fields. The classical results are recovered when integer dimensional space is considered. The proposed solution is useful for deriving electromagnetic modes of fractal structures.