Theoretical studies on the transmission and reflection properties of metallic planar fractals

We describe a systematic finite-difference-time-domain study on the electromagnetic (EM) characteristics of a specific type of planar metallic fractal patterns. These fractals are shown to totally reflect EM waves at a series of frequencies; between any two reflection frequencies there can be total transmission at some particular frequency. We show that both reflection and transmission are induced by local resonances, and develop an effective medium model to reproduce the simulation results. A double stack of 90degrees-rotated fractals is shown to exhibit absolute band gaps independent of both the polarization and incidence angles. In particular, the size of the band gaps can be significantly enlarged by multilayer stacking, and the fractal sample size can be significantly smaller than the relevant band gap wavelength.