Investigation of beam splitter in a zero-refractive-index photonic crystal at the frequency of Dirac-like point.

The Dirac-like cone dispersion of the photonic crystal induced by the three-fold accidental degeneracy at the Brillouin center is calculated in this paper. Such photonic crystals can be mapped to zero-refractive-index materials at the vicinity of the Dirac-like point frequency, and utilized to construct beam splitter of high transmission efficiency. The splitting ratio is studied as a function of the position of the input/output waveguides. Furthermore, variant beam splitters with asymmetric structures, bulk defects, and some certain bending angles are numerically simulated. Finally, we show that 1 × 2 to 1 × N beam splitting can be realized with high transmission efficiency in such a zero-refractive-index photonic crystal at the frequency of Dirac-like point. The proposed structure could be a fundamental component of the high density photonic integrated circuit technique.