Abstract
A Menger sponge structure is a typical 3D fractal. Such the fractal structure made of dielectric materials, which we call the photonic fractal, can localize electromagnetic waves with specific frequencies. In this study, we fabricated Menger sponge structures composed of polyester resin including TiO 2 particles with different contents in order to investigate the relation between the dielectric constant of the fractal structure and the localized frequency of electromagnetic wave. They were formed by impregnating the TiO 2 /polyester slurry into epoxy molds. The mold was designed to have a negative shape of Menger sponge structure using 3D-CAD software and formed by stereolithography. Electromagnetic properties were measured by using a network analyzer, horn antenna, and mono-pole antennas. The localizations were observed for TiO 2 /polyester Menger sponge structures. Calculated localized frequencies by an empirical equation with a function of the dielectric constant of a fractal structure and the fractal geometry showed good agreements with the measured frequencies.
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