  This paper considers the propagation of TE-modes in photonic crystal
waveguides. The waveguide is created by introducing a linear defect into a
periodic background medium. Both the periodic background problem and the
perturbed problem are modelled by a divergence type equation. A feature of our
analysis is that we allow discontinuities in the coefficients of the operator,
which is required to model many photonic crystals. It is shown that arbitrarily
weak perturbations introduce spectrum into the spectral gaps of the background
operator.
