  We consider a one-dimensional photonic crystal composed of alternating layers
of isotropic and anisotropic dielectric materials. Such a system has different
band structures for different polarizations of light. We demonstrate that if an
anisotropic defect layer is inserted into the structure, the crystal can
support an optical bound state in the continuum. By tilting the principle
dielectric axes of the defect layer relative to those of the photonic crystal
we observe a long-lived resonance in the transmission spectrum. We derive an
analytical expression for the decay rate of the resonance that agrees well with
the numerical data by the Berreman anisotropic transfer matrix approach. An
experimental set-up with a liquid crystal defect layer is proposed to tune the
Q-factor of the resonance through applying an external electric field. We
speculate that the set-up provides a simple and robust platform for observing
optical bound states in the continuum in the form of resonances with tunable
Q-factor.
