Top-down metamaterial design for enhancing extraordinary field focusing of electromagnetic and acoustic waves

Abstract

Since their discovery by Ebbesen in 1998, extraordinary transmission and field enhancement of photonic waves have comprised a popular and important area of photonics research, including studies of light from a wide range of spectra (visible, infrared, THz, microwave) transmitted through various aperture geometries (Bow-tie, slit, hole antenna, NSOM, metamaterials). Extraordinary transmission of electromagnetic waves has been assumed to be impossible in the case of a focusing area size smaller than the metallic skin-depth, as the waves interact with metallic electrons only within the skin-depth of the surface. The first part of this thesis addresses the extremely challenging problem of 3 mm wavelength light impinging on a 70 nm (λ/40,000) wide nanogap or nanowire, smaller than the skin-depth of 250 nm. Comparing effects of the complementary nanogap and nanowire structures, which should be identical by Babinets principle, the saturation point of the electric field enhancement in the nanogap was at the Thomas-Fermi length (<1 nm), much smaller than the skin-depth. The magnetic field enhancement in the nanowire was 100,000, which, while large, is much less than the electric field enhancement in the nanogap of 1,000,000

thus, Babinets principle does not hold in the extreme skin-depth domain. The extreme focusing in the nanogap could be utilized in nonlinear optical devices or nanosensor systems. In the second part of this thesis, I designed metamaterials to enhance the focusing efficiency. For example, matched zero-index metamaterials could erase the effective space to increase collection of the light beyond the λ-zone limit. To design such metamaterials, I propose an entirely new top-down design strategy of the meta-atom, where the target εeff and μeff are first specified, and then, the design parameters are determined, inspired by fundamental oscillations of the elementary particle associated with the wave. To decouple the fundamental wave parameters εeff and μeff, envisaged by Pendry as an ideal platform for top-down and reconfigurable design of meta-atoms, I separated the anisotropic permittivity of the hypothetic meta-atom along radial (εr) and angular (εθ) directions. I analytically solved the inverse problem of the proposed structure design for the desired wave parameters

the design parameters (εr, εθ) were determined to achieve matched zero-index properties (εeff = μeff = 0). I numerically demonstrated extraordinary transmission through a nanogap, 50 times greater than the previous ?-zone limit, utilizing the designed matched zero-index meta-atom. Finally, I extended these concepts from electromagnetics to acoustics using the duality relation between the electromagnetic (permittivity: ε, permeability: μ) and acoustic (density: ρ, compressiblity: B-1) wave parameters. As in the electromagnetic case, it is possible to decouple and independently control acoustic parameters ρ and B-1 by separating the membrane vibrations along the linear and radial directions. Parameter mapping of the analytical results shows the orthogonality between (ρ, B-1), and separated membrane parameters (mO, mI), and visualizes the possibility of top-down design. Independent control of bianisotropy ξ which arises from structural asymmetry, is realized theoretically and experimentally. Super-focusing and scattering through an asymmetric waveguide are demonstrated using bianisotropic pressure-velocity conversion.