  We show that point defects in two-dimensional photonic crystals can support
bound states in the continuum (BICs). The mechanism of confinement is a
symmetry mismatch between the defect mode and the Bloch modes of the photonic
crystal. These BICs occur in the absence of bandgaps and therefore provide an
alternative mechanism to confine light. Furthermore, we show that such BICs can
propagate in a fiber geometry and exhibit arbitrarily small group velocity
which could serve as a platform for enhancing non-linear effects and
light-matter interactions in structured fibers.
