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

Pingping Qiu,Jiao-Qing Pan,Houbo Chen,Jia-Xian Wang,Junbo Ren,Weibin Qiu,Zhili Lin,Qiang Kan

doi:10.1038/s41598-017-10056-z

Pingping Qiu, Jiao-Qing Pan + Show 6 more

Open Access

https://doi.org/10.1038/s41598-017-10056-z

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Abstract

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.

Highlights

In recent years, metamaterials with zero-refractive-index have attracted considerable attention due to their intriguing properties and novel applications
The band structure of the all-dielectric photonic crystals (PCs) with r = 0.1433a is plotted in Fig. 1(a), where we can see that two bands linearly intersect with an additional flat band at the Brillouin zone (BZ) center, resulting in a three-fold degenerate point marked with “D”, which is the so-called Dirac-like point[26]
To have a more clear view of the Dirac-like cone dispersion, we zoom in the band structure near the BZ center as shown in Fig. 1(b), where two branches with linear dispersions intersect at the degenerate point D, through which point there is a another flat band resulting in the Dirac-like cone