Abstract
Hyperbolic materials can sustain propagating modes with very large wave vectors and are thus characterized by a very large density of states. In practice, it is possible to mimic a hyperbolic material using a periodic stack of metallic and dielectric layers that can support surface plasmons with large wave vectors. This raises the question of the nature of the modes in the hyperbolic metamaterial medium and their connection to surface plasmons. Here, we address this question experimentally and theoretically by considering an interface separating a hyperbolic metamaterial from a vacuum. We image the local density of states outside the medium at different distances. By carefully analyzing the spectral and spatial structure of the local density of states as the sample is approached from the vacuum, we establish the connection between the two points of view. We find that the homogenized hyperbolic metamaterial picture is valid outside the material for distances larger than a∕2π, where a is the period of the multilayer. For smaller distances, the local density of states displays spatial and spectral peaks pointing to the role of surface plasmons propagating along the interfaces in the layer stack.