Plasmonic Metamaterials From Fractal Structure

Structured metals have received great attentions in the past decades, enabling the exotic electromagnetic (EM) phenomena, such as extraordinary optical transmission (EOT) which refers to greatly enhanced transmission of light through subwavelength hole arrays or apertures in an opaque metallic film. The existence of EOT usually relies on either (spoof) surface plasmon or local resonance on the structured metallic surface which are both critically related to periodicity of the hole array and geometric shape of the apertures.In this thesis, we introduce a deeply subwavelength aperture with H-fractal shape and without loading high-index dielectric to the structured metallic plate, and show a strong diamagnetic response of μeff～0. In particular, such～0 permeability not only can be much less than the area fraction of the apertures, beyond the conventional geometrical relation, but also happens at broadband microwave frequencies. We demonstrate a design of structured metal with 64% hollow area, which gives rise to a close-to-zero strong diamagnetic permeability with the 175% relative bandwidth.When a number of the metallic plates with H-fractal slits are cascaded, their resonant modes will couple together, the transmission bands would be developed in a way analogue to the formation of miniband in a semiconductor superlattice.We show the analogy can be extended further by investigating the photonic Wannier-Stark ladder (PWSL) in the system of coupled EM cavities, where the biased potential effect is mimicked by imposing the gradient variation of refractive index. A numerical model is constructed, using a stack of metallic plates slotted with subwavelength H-fractal apertures. By calculating the transmission, we have observed that the transmission peaks of the ladder states have the equidistant frequency spacing in the spectrum, i.e. their frequencies (eigen energies) showing an arithmetical series, in the case of small gradient. Particularly, the frequencies of the peaks evolve into a geometrical series in the case of large gradient, which points out the generalized PWSL with geometrically progressed energies.Besides H-fractal apertures, we also study the EM characteristics of metallic Hilbert fractal curves in the microwave frequency domain. Its resonant modes are generated by the complex interaction between electric/magnetic field and the structure after the TEM wave is incident normally on the Hilbert structure, and the fundamental resonance is found being induced by magnetic flux. We summarize the subwavelength characteristics between the varying fractal order of the samples and the relevant localized resonances.