  We investigate the optical properties of sub-wavelength layered
metal/dielectric structures, also known as hyperbolic metamaterials (HMMs),
using exact analytical Kronig Penney (KP) model. We show that hyperbolic
isofrequency surfaces exist for all combinations of layer permittivities and
thicknesses, and the largest Purcell enhancements (PE) of spontaneous radiation
are achieved away from the nominally hyperbolic region. Detailed comparison of
field distributions, dispersion curves, and Purcell factors (PF) between the
HMMs and Surface Plasmon Polaritons (SPPs) guided modes in metal/dielectric
waveguides demonstrates that HMMs are nothing but weakly coupled gap or slab
SPPs modes. Broadband PE is not specific to the HMMs and can be easily attained
in single thin metallic layers. Furthermore, large wavevectors and PE are
always combined with high loss, short propagation distances and large
impedances; hence PE in HMMs is essentially a direct coupling of the energy
into the free electron motion in the metal, or quenching of radiative lifetime.
PE in HMMs is not related to the hyperbolicity per se but is simply the
consequence of the strong dispersion of permittivity in the metals or polar
dielectrics, as our conclusions are relevant also for the infrared HMMs
occurring in nature. When it comes to enhancement of radiating processes and
field concentrations, HMMs are not superior to far simpler plasmonic
structures.
