Transverse Electromagnetic Modes of Menger Sponge
Keywords:
Fractional dimension, menger spone, transverse electromagnetic.Abstract
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.
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