Spectral analysis of Serpinskij carpet-like prefractal waveguides and resonators

Exact results on some modal properties of waveguides and resonators is studied, whose geometry is derived from "Serpinskij carpet-like" prefractals (Serpinskij carpet and sponge; Menger sponge). The study is biased to the closed-form computation of specific resonances and eigenmodes (called "dia-periodic"), and to the relation existing between their topology and the existence of a finite set of transverse electromagnetic modes.