3D Printing of Fractal Objects

"Fractal is the term which describes rough and irregular structures with self-similarity such that the local

configuration is similar to the whole configuration [1]. Fractal structures have no periodicity and no translational

symmetry like crystal structures. Interaction of optical, electromagnetic, and acoustical waves with fractal or

quasi-periodic structures has been of theoretical and practical interest in recent years. However, studies

concerning the localization of electromagnetic waves in these structures have been restricted to one or two

dimensions [2-6]. A 3D fractal structure is necessary to completely localize light or electromagnetic waves.

Nevertheless, 3D fractal structures have not been fabricated probably due to the difficulties of construction.

Recently, we have succeeded in the fabrication of 3D fractal structures called Menger sponges, which are made

of dielectric media such as epoxy and ceramics, and found a significant feature in that the incident microwave

is strongly localized in the fractal with very large attenuations both in reflectance and transmittance at the

same frequency [7,8]. We have named such fractals as photonic fractals because no other materials which can

localize electromagnetic waves in the 3D fractal form is known. Photonic fractals may have large potential

applications in communication, information, energy, sensing, medical care, and other fields. This paper reports

on the design and fabrication of 3D fractals using CAD/CAM stereolithography, electromagnetic wave

responses for such fractal structures made of polymer, ceramic, and metal materials, together with expected

applications."