  Time-harmonic electromagnetic plane waves in anisotropic media can exhibit
complex-valued wavevectors (with nonzero real and imaginary parts) even in the
absence of material dissipation. These peculiar modes, usually referred to as
"ghost waves," hybridize the typical traits of conventional propagating and
evanescent waves, displaying both phase accumulation and purely reactive
exponential decay away from the direction of power flow. Their existence has
been predicted in several scenarios, and has been recently observed
experimentally in the form of surface phonon polaritons with complex-valued
out-of-plane wavevectors propagating at the interface between air and a natural
uniaxial crystal with slanted optical axis. Here, we demonstrate that ghost
waves can arise also in lower-dimensional flat-optics scenarios, which are
becoming increasingly relevant in the context of metasurfaces and in the field
of polaritonics. Specifically, we show that planar junctions between isotropic
and anisotropic metasurfaces can support "ghost line waves" that propagate
unattenuated along the line interface, exhibiting phase oscillations combined
with evanescent decay both in the plane of the metasurface (away from the
interface) and out-of-plane n the surrounding medium. Our theoretical results,
validated by finite-element numerical simulations, demonstrate a novel form of
polaritonic waves with highly confined features, which may provide new
opportunities for the control of light at the nanoscale, and may find potential
applications in a variety of scenarios, including integrated waveguides,
nonlinear optics, optical sensing and sub-diffraction imaging.
