Nonlocal dispersion anomalies of Dyakonov-like surface waves at hyperbolic media interfaces

•We explore Dyakonov surface waves propagating obliquely at the interface between an insulator and a hyperbolic bandgap metamaterial.•We found unexpected favorable conditions for the existence of such surface waves.•The finite element method is used to investigate the peculiarities of this new family of DSWs.

Dyakonov-like surface waves (DSWs) propagating obliquely on an anisotropic nanostructure have been theoretically proved in a few cases including 2D photonic crystals and metal-insulator (MI) layered metamaterials. Up to now, the long-wavelength approximation has been employed in order to obtain effective parameters to be introduced in the Dyakonov equation, which is largely restricted to material inhomogeneities of a few nanometers when including metallic elements. Here, we explore DSWs propagating obliquely at the interface between an insulator and a hyperbolic metamaterial, the latter consisting of a 1D MI bandgap grating using realistic slab sizes. We found unexpected favorable conditions for the existence of such surface waves. The finite element method is used to investigate the peculiarities of this new family of DSWs.