Hyperbolic metamaterials: beyond the effective medium theory

Abstract

Sub-wavelength layered metal/dielectric structures whose effective permittivities for different polarizations have different signs are known as hyperbolic metamaterials (HMMs). It is believed they are unique in their ability to support electromagnetic waves with very large wavevectors and, therefore, large densities of states, leading to a strong Purcell enhancement (PE) of spontaneous radiation. To verify this conventional wisdom, we use an analytic Kronig–Penney (KP) model and discover that hyperbolic isofrequency surfaces exist for all combinations of layer permittivities and thicknesses, and the strongest PE of radiation is achieved away from the nominally hyperbolic region. 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 the radiative lifetime. PE in HMMs is not related to the hyperbolicity, per se, and is simply the consequence of strong dispersion of the permittivity in metals or polar dielectrics, as our conclusions are relevant also for the infrared HMMs that occur in nature. Moreover, detailed comparison of field distributions, dispersion curves, and Purcell factors between the HMM and surface plasmon polariton (SPP) guided modes in metal/dielectric waveguides demonstrates that HMMs are nothing but weakly coupled gap or slab SPP modes. Broadband PE is not specific to the HMMs and can be just as easily attained in single or double thin metallic layers. When it comes to enhancement of radiating processes and field concentrations, HMMs are in no way superior to far simpler plasmonic structures.