Disclosed herein are exemplary embodiments of materials and structures that have a negative refractive index. For example, one exemplary embodiment is a waveguide structure comprising a first waveguide border element having a first substantially planar surface, and a second waveguide border element spaced apart from the first waveguide border element and having a second substantially planar surface. This exemplary embodiment further comprises a core material positioned between the first substantially planar surface and the second substantially planar surface. The core material has a positive in-plane dielectric constant and a negative perpendicular-to-plane dielectric constant. Furthermore, the first waveguide border element, the second waveguide border element, and the core material form a waveguide exhibiting a negative index of refraction for electromagnetic radiation in a frequency range.