Optical metamaterials have presented an innovative method of manipulating light. Hyperbolic metamaterials have an extremely high anisotropy with a hyperbolic dispersion relation. They are able to support high-k modes and exhibit a high density of states which produce distinctive properties that have been exploited in various applications, such as super-resolution imaging, negative refraction, and enhanced emission control. Here, state-of-the-art hyperbolic metamaterials are reviewed, starting from the fundamental principles to applications of artificially structured hyperbolic media to suggest ways to fuse natural two-dimensional hyperbolic materials. The review concludes by indicating the current challenges and our vision for future applications of hyperbolic metamaterials.

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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.

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