Ghost Waves in Anisotropic Materials: negative refractive index and evanescent field enhancement in lossless media

We show that transparent dielectrics with strong optical anisotropy support a new class of 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 non-integrable dynamical systems. Similarly to the regular evanescent fields, ghost waves support high transverse wavenumbers, but in addition to the exponential decay show oscillatory behavior in the direction of propagation. Ghost waves can be resonantly coupled to the incident evanescent waves, which then grow exponentially through the anisotropic media - as in the case of negative index materials.As ghost waves are supported by transparent dielectric media, they are free from the "curse" of material loss that is inherent to conventional negative index composites.