Experimental demonstration of broadband negative refraction at visible frequencies by critical layer thickness analysis in a vertical hyperbolic metamaterial

This work presents a vertical hyperbolic metamaterial (vHMM) consisting of a vertically stacked metal-dielectric multilayer that operates in the visible spectrum. The vHMM is designed by exploiting the relation between negative refraction and effective permittivity along the perpendicular direction of the layers (epsilon(perpendicular to)). When a vHMM has a high loss tangent defined by tan delta(perpendicular to) = Im(epsilon(perpendicular to))/Re(epsilon(perpendicular to)), even a vHMM composed of relatively thick layers can generate negative refraction. A fabricable vHMM composed of gold and copolymer resist (EL8) which exhibits negative refraction at the wavelengths between 450 and 550 nm is designed using critical layer thickness analysis. The largest negative refraction is observed at the wavelength of 500 nm, where the angle of refraction reaches -1.03 degrees. The corresponding loss tangent and equivalent refractive index are 1.08 and -0.47, respectively. However, negative refraction is not observed at the wavelengths longer than 550 nm due to low tan delta(perpendicular to). We uncover that the tan delta(perpendicular to) of a vHMM is the dominant condition for generating negative refraction rather than the ratio of layer thickness to wavelength.

Automated summary

This paper presents a vertically stacked metal-dielectric multilayer vertical hyperbolic metamaterial (vHMM) that operates in the visible spectrum. The research explores the relationship between negative refraction and effective permittivity, specifically focusing on the importance of the loss tangent in generating negative refraction. The designed vHMM exhibits negative refraction in the wavelengths between 450 and 550 nm, reaching the largest negative refraction at 500 nm wavelength.