title: Localization of electromagnetic waves in three-dimensional fractal cavities.
abstract: Three-dimensional fractals called the Menger sponge, with a fractal dimension D=log(20/log(3, were fabricated from epoxy resin by stereolithography. Clear attenuation of both reflection and transmission intensity was observed at 12.8 GHz for a cubic specimen with an edge size of 27 mm that was constructed up to the third stage of the self-similar patterns. The electromagnetic field was found to be confined in the central part of the specimen at this frequency. The localization is not caused by the presence of a photonic band gap as in photonic crystals but should be attributed to a singular photon density of states realized in the fractal structure. This is the first report on such localization of electromagnetic waves in three-dimensional fractal cavities.
authors.affiliation: Department of Physics, Faculty of Science, Shinshu University, Matsumoto, Nagano 390-8621, Japan. wada@azusa.shinshu-u.ac.jp
authors.forename: Mitsuo Wada
authors.initials: MW
authors.lastname: Takeda
authors.forename: Soshu
authors.initials: S
authors.lastname: Kirihara
authors.forename: Yoshinari
authors.initials: Y
authors.lastname: Miyamoto
authors.forename: Kazuaki
authors.initials: K
authors.lastname: Sakoda
authors.forename: Katsuya
authors.initials: K
authors.lastname: Honda