Strong localization of microwave in photonic fractals with Menger-sponge structure

Abstract

Photonic fractal with self-similar structure of dielectric medium can strongly localize the electromagnetic wave energy in the three-dimensional fractal structure. We have fabricated Menger-sponge fractal structures of epoxy by using stereolithography. Titania–silica particles were dispersed into the epoxy to increase the dielectric constant and decrease the dielectric loss. The samples have square holes of 1, 3, 9 and 27 mm in edge length through the cubic body of 81 mm. Four types of Menger-sponge samples with fractal stages 1–4 were subjected for measurement of microwave responses. The both reflection and transmission amplitudes were attenuated simultaneously at frequencies of 9.5, 10.5, 12.0 and 13.5 GHz for each sample with fractal stages 1, 2, 3 and 4, respectively. The electromagnetic field amplitudes in the air holes measured by inserting a mono-pole antenna probe confirmed the strong localization of the electromagnetic wave in the central air cavity. The localized mode frequency can be calculated using the sample size, number of stage, and the effective dielectric constant. The localization efficiency increased according to the fractal stage number.