We show that dielectric waveguides formed by materials with strong optical anisotropy support electromagnetic waves that combine the properties of propagating and evanescent fields. These “ghost waves” are created in tangent bifurcations that “annihilate” pairs of positive- and negative-index modes and represent the optical analogue of the “ghost orbits” in the quantum theory of nonintegrable dynamical systems. Ghost waves can be resonantly coupled to the incident evanescent field, which then gr
