Localization of electromagnetic wave in 3D periodic and fractal structures

Localization or confinement of electromagnetic or optical waves is reviewed briefly in respect to the wave interaction with the specific structures of periodic, random, and fractal (self-similar) geometries, which can enhance strong interference, scattering, and resonance of waves. The localization of microwave in photonic crystals with diamond structure and in photonic fractals with Menger sponge structure of dielectric media is reported and discussed about the difference of localization behaviors. These 3D structures are fabricated easily from liquid photosensitive resins or ceramic dispersed ones by a CAD/CAM stereo-lithography. The localization in photonic fractals is supported with several measurements of transmission, 90 degrees wave scattering, electric field intensity profile, and FDTD (finite-difference time-domain) simulation for localized modes. An empirical equation to predict the localization frequencies shows good agreements with measured results as well. The localization in a photonic crystal can be explained by Bragg scattering, while that in a photonic fractal by resonance in the fractal cavity.