Waveguide stopped light mediated by mode transitions

Hyperbolic metamaterials (HMMs) are uniaxial materials that have hyperbolic dispersion curves. There are two types of hyperbolic metamaterials, type I that is described by a permittivity tensor with ϵ_|| > 0 and ϵ > 0, and type II that has ϵ_|| > 0 and ϵ_± < 0. Planar waveguides with hyperbolic materials have been mostly studied with propagation direction along the principal axis of the dielectric tensor only. Such studies showed that modes feature anomalous ordering in such a way that cut-off appears for lower order modes as light frequency increases. Interestingly, stopped light featuring null group velocity at specific wavelengths has been predicted for modes near cut-off in type II HMMs planar waveguides with optical axis (OA) oriented along the propagation direction [1]. Here, we theoretically study light propagation in type II HMMs planar waveguides for any orientation φ of the OA contained in a plane parallel to the waveguides interfaces. The results shows that a change in the wavelength only changes the OA direction φ at which stopped light exist. The process is a consequence of the lack of mode cut-off and it is caused by a mode spectroscopy transition from hyperbolic modes with anomalous order propagating along the OA (φ = 0°), to modes with normal order, propagating orthogonally to the OA (φ = 90°).