Hyperbolic Metamaterials and Coupled Surface Plasmon Polaritons: comparative analysis

Abstract: 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.