Critical Layer Thickness Analysis of Vertically Stacked Hyperbolic Metamaterials for Effective Negative Refraction Generation

Abstract

Vertically stacked narrow metal‐dielectric multilayered structures known as vertical hyperbolic metamaterials (vertical HMMs) are proposed for broadband negative refraction. The thickness of each layer is required to be subwavelength for effective medium theory (EMT) to be applicable. Therefore, each layer should be thin, forcing the aspect ratio to become extremely high. This requirement makes the fabrication of vertical HMMs difficult. Thus, it is important to determine the limit of the layer thickness for the realization of vertical HMM. In this study, the critical layer thicknesses of vertical HMMs are investigated numerically at the wavelengths of 400, 500, 600, and 700 nm. It is concluded that the critical layer thicknesses for both vertical and horizontal HMMs depend on the permittivity along the perpendicular direction of the layers. The maximum critical layer thickness of vertical HMMs, with a value of 0.22, is produced by a structure composed of gold and silicon dioxide at the wavelength of 500 nm, while the critical layer thickness tends to be smaller if silver is employed. It is believed that this study can provide a useful database as quantitative indicators which can be exploited in designing nanostructures using EMT.

Hyperbolic metamaterials: fusing artificial structures to natural 2D materials

“…5b). A numerical study of the critical layer thickness of vHMMs in the visible region has been reported [125]. A variety of vHMMs composed of various materials have been numerically investigated to determine the critical layer thickness of the potential for negative refraction utilization.…”

Geometric and physical configurations of meta‐atoms for advanced metasurface holography

“…For example, chiral metamaterials, consisting of meta‐atoms lacking any mirror symmetry planes, can selectively absorb left or right circularly polarized light (LCP and RCP, respectively) 18–26 . Also, hyperbolic metamaterials, which are composite materials made up of dielectric and metallic subwavelength‐layers, are able to possess high wavevector modes inside 27–33 …”

A planar ultraviolet objective lens for optical axis free imaging nanolithography by employing optical negative refraction

“…Currently, except for a positive uniaxial crystal, 13 a uniaxially anisotropic material with a hyperbolic dispersion relationcommonly known as a hyperbolic metamaterial (HMM) has become a fascinating candidate for achieving optical negative refraction. [14][15][16] Especially, a planar metal/dielectric single-periodic multilayer at lens operating at ultraviolet (UV) wavelength was proposed, 17 which demonstrates a clear focus in air 350 nm away from the surface of the at lens through simulation and experiment. However, to the best of our knowledge, there are no reports about studies of planar UV objectives based on optical negative refraction for nanolithography applications.…”