We present a theoretical condition for achieving three-dimensional self-collimation of light in a photonic crystal. Such effects provide a very interesting mechanism for developing integrated circuits in 3D crystals that can be synthesized in a large scale. We also show that in a dielectric waveguide with a photonic crystal core, the modal properties are very unusual. In particular, a single-mode waveguide for the fundamental mode with a large core and a strong confinement can be realized. This is potentially important for suppressing modal competition in laser structures.
The reflection phenomena of a light beam incident upon the interfaces between the crystal and a uniform dielectric are explored in this paper. We show that neither the phase velocity nor the group velocity directions of the reflected beam satisfy Snell’s law and we prove that a generalized wave-vector conservation relation still applies even when the interface is not aligned with special crystal directions. Moreover, the system exhibits remarkable and unusual reflection effects. In particular, total internal reflection is absent except at discrete angular values. The direction of reflection beam can also be pinned along special crystal directions, independent of the orientation of the interface. And finally, at
glancing incidences, strong backward reflection may occur. These effects may be important for creating integrated photonic circuits, and for on-chip image transfer.