  Consider a plane monochromatic wave incident on a semi-infinite periodic
structure. What happens if the normal component of the transmitted wave group
velocity vanishes? At first sight, zero normal component of the transmitted
wave group velocity simply implies total reflection of the incident wave. But
we demonstrate that total reflection is not the only possible outcome. Instead,
the transmitted wave can appear in the form of a frozen mode with very large
diverging amplitude and either zero, or purely tangential energy flux. The
field amplitude in the transmitted wave can exceed that of the incident wave by
several orders of magnitude. There are two qualitatively different kinds of
frozen mode regime. The first one is associated with a stationary inflection
point of electromagnetic dispersion relation. This phenomenon has been analyzed
in our previous publications. Now, our focus is on the frozen mode regime
related to a degenerate photonic band edge. An advantage of this new phenomenon
is that it can occur in much simpler periodic structures. This spectacular
effect is extremely sensitive to the frequency and direction of propagation of
the incident plane wave. These features can be very attractive in a variety
practical applications, such as higher harmonic generation and wave mixing,
light amplification and lasing, highly efficient superprizms, etc.
