Vortices Formed by Two Counter-Propagating Waves for Surface Phonon Polaritons with Material Losses

We examine the surface phonon polaritons established on resonance between lossy silicon carbide and vacuum over the Reststrahlen frequency range. To this goal, we investigate two waves counter-propagating along a planar material interface in terms of the orbital and spin parts of the Poynting vector. Vortices of the spin part are thus found to be generated near the collision point of the two waves. In addition, vortex pairs of opposite circulations are identified near the material interface. The locality of the electric permittivity plays an essential role in enabling our simple analysis by neglecting the spatial propagations of phonons while keeping the material damping. The resulting dynamics of the total displacement field turns out to be loss-free in the middle of the lossy dynamics of the other field variables, thus exhibiting a superfluid-like feature in an otherwise normal fluid.