The beam splitting in the photonic crystal at a degenerate state

In this paper, using the plane-wave expansion and finite difference time-domain methods, the photons behavior in the photonic crystal is investigated. Theoretically, when a polarized wave is incident from the background medium to the photonic crystal, the beam propagation directions in the photonic crystal determined by two methods are approximately same. But in this paper, the results exhibit that there is an additional direction obtained by the finite difference time-domain method compared with the plane-wave expansion. Considering basic physical mechanism of the photon behavior, the present work circumvents the electromagnetic field distribution in the photonic crystal at a degenerate state, which can reasonably explain the phenomenon. Finally, it shows that a photonic crystal can be properly designed to achieve double refraction simultaneously at one frequency, which can also offer new thoughts and foundation for the novel beam splitter that applied to many optical systems.