After a report on strange electromagnetic resonances emerging in an isotropic paraelectric Menger sponge (MS) now known as a photonic fractal, vigorous studies began to reveal their properties. However, the mechanics of how the resonances occur is still unknown. This report focuses on the findings that the resonances can be perturbation-theoretically identified as those originally occurring in an isolated dielectric cube, and that they arise within band gaps and uncouple with Bloch modes for a certain multiperiodic lattice. This interpretation is justified by the fact that the MS can be considered as a cube embedded in the lattice rather than the outcome of conventional recursive fractal structuring operations. An experimental formula for resonance conditions already reported can be derived from this interpretation.
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