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 (ε ⊥). When a vHMM has a high loss tangent defined by tan δ ⊥ ≡ Im(ε ⊥)/Re(ε ⊥), 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°. 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 δ ⊥. We uncover that the tan δ ⊥ of a vHMM is the dominant condition for generating negative refraction rather than the ratio of layer thickness to wavelength.