Effective-medium approach to planar multilayer hyperbolic metamaterials:Strengths and limitations

摘要

We express the optical properties of multilayered hyperbolic metamaterials (HMMs) in terms of the Fresnelnreflection coefficients at the boundary between the metamaterial and the ambient medium. Formation of anband of bulk propagating modes in HMMs located far outside the lightcone of homogeneous isotropic media isndemonstrated. Exotic behavior of HMMs, such as the broadband Purcell effect and suppressed outward scattering,nis reproduced. Conditions under which a metal-dielectric multilayer can be approximated by a homogeneousneffectivemedium with extreme anisotropy (indefinite medium) are derived. It is shown that real multilayer HMMsnusually have a smaller Purcell factor than the corresponding effective medium; however, the reverse scenario isnshown to be possible due to an intermediary role of short-range surface plasmon excitations in the outermostnmetal layer in a metal-dielectric multilayer.