  We analyze the propagation of waves in unbounded photonic crystals, the waves
are described by a Helmholtz equation with $x$-dependent coefficients. The
scattering problem must be completed with a radiation condition at infinity,
which was not available for $x$-dependent coefficients. We develop an outgoing
wave condition with the help of a Bloch wave expansion. Our radiation condition
admits a (weak) uniqueness result, formulated in terms of the Bloch measure of
solutions. We use the new radiation condition to analyze the transmission
problem where, at fixed frequency, a wave hits the interface between free space
and a photonic crystal. We derive that the vertical wave number of the incident
wave is a conserved quantity. Together with the frequency condition for the
transmitted wave, this condition leads (for appropriate photonic crystals) to
the effect of negative refraction at the interface.
