Takeda Mitsuo Wada, Kirihara Soshu, Miyamoto Yoshinari, Sakoda Kazuaki, Honda Katsuya
Department of Physics, Faculty of Science, Shinshu University, Matsumoto, Nagano 390-8621, Japan.
Phys Rev Lett. 2004 Mar 5;92(9):093902. doi: 10.1103/PhysRevLett.92.093902. Epub 2004 Mar 4.
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.
通过立体光刻技术由环氧树脂制造出了分形维数D = log(20)/log(3)的三维分形结构——门格海绵体。对于一个边长为27毫米、构建到自相似图案第三阶段的立方体样品，在12.8吉赫兹时观察到反射和透射强度都有明显衰减。在这个频率下，发现电磁场被限制在样品的中心部分。这种局域化不是像光子晶体那样由光子带隙的存在引起的，而应归因于分形结构中实现的奇异光子态密度。这是关于三维分形腔中电磁波这种局域化的首次报道。
