Analysis of electromagnetic response of 3-D dielectric fractals of menger sponge type

Experimental studies and finite-difference time-domain simulations of electromagnetic (EM) response of the second-stage Menger sponge dielectric structures have been performed with different types of excitation in order to gain deeper insight into the phenomenon of EM wave localization in these fractals. Analysis of simulated amplitude distributions of electric field oscillations in the Menger sponges has revealed bandgap-like effects caused by resonances in the front part of the structures, as well as formation of the full-wave resonance mode in the central cavity at the localization frequency. It is demonstrated that penetration of the waves inside the structure at the localization frequency leads to equalizing of the EM response from different parts of the 3-D fractal, however, no high-Q eigenmode is formed in the second-stage Menger sponge. Simulations of the modified fractal structures have been used to show the potential of formation of a bandgap with defect-related localized photon states by 3-D fractals. Index Terms--Ceramics, electromagnetic (EM) fields, finite-difference time-domain (FDTD) method, fractals, resonance.