  Wave propagation in spatially periodic media, such as photonic crystals, can
be qualitatively different from any uniform substance. The differences are
particularly pronounced when the electromagnetic wavelength is comparable to
the primitive translation of the periodic structure. In such a case, the
periodic medium cannot be assigned any meaningful refractive index. Still, such
features as negative refraction and/or opposite phase and group velocities for
certain directions of light propagation can be found in almost any photonic
crystal. The only reservation is that unlike hypothetical uniform left-handed
media, photonic crystals are essentially anisotropic at frequency range of
interest. Consider now a plane wave incident on a semi-infinite photonic
crystal. One can assume, for instance, that in the case of positive refraction,
the normal components of the group and the phase velocities of the transmitted
Bloch wave have the same sign, while in the case of negative refraction, those
components have opposite signs. What happens if the normal component of the
transmitted wave group velocity vanishes? Let us call it a "zero-refraction"
case. At first sight, zero normal component of the transmitted wave group
velocity implies total reflection of the incident wave. But we demonstrate that
total reflection is not the only possibility. Instead, the transmitted wave can
appear in the form of an abnormal grazing mode with huge amplitude and nearly
tangential group velocity. This spectacular phenomenon is extremely sensitive
to the frequency and direction of propagation of the incident plane wave. These
features can be very attractive in numerous applications, such as higher
harmonic generation and wave mixing, light amplification and lasing, highly
efficient superprizms, etc.
