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We report photonic properties of subwavelength three-dimensional 3D metallic H-shaped fractals. The fractal structure supports localized resonances with relevant wavelength over ten times the sample size. Owing to the anisotropy inherent to the fractal geometry, the resonances and their induced band gaps are polarization dependent. The measured microwave transmission spectra agree well with simulations, and show the anisotropic response to be well described by an effective dielectric tensor. Using the three-dimensional H fractal as the basic unit, a microwave photonic crystal was fabricated, and its band-gap characteristics shown to display unique features of hybridization between local resonances and Bragg scattering. A photonic crystal of 3D fractals is an excellent microwave analog to an anisotropic electronic solid consisting of atoms or molecules with localized discrete energy levels.

Three-dimensional metallic fractals and their photonic crystal characteristics