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摘要

设计了一种由椭圆介电柱子组成的正方晶格光子晶体结构. 通过调节椭圆柱子的大小和放置角度, 在布里渊区中心同时实现两个不同频率的双重偶然简并, 并获得两个不同波段的半狄拉克锥. 更有趣的是, 这两个半狄拉克锥沿椭圆柱子长轴和短轴两个方向表现出的线性和非线性色散关系正好相反, ${\boldsymbol{k}} \cdot {\boldsymbol{p}}$ 微扰理论也进一步证实了这种奇异的色散关系. 数值计算结果表明在两个半狄拉克点频率附近, 本文所设计的正方晶格光子晶体在线性色散所在方向上等效为阻抗匹配的双零折射率材料, 而在非线性色散所在方向上只能等效为单零折射率材料, 即沿椭圆柱子长轴和短轴两个方向的等效零折射率展现出差异性. 而两个不同波段的半狄拉克锥所对应的这种等效零折射率的各向异性截然相反, 因此可利用“Y”型光子晶体板将两种不同频率的电磁波成功分离.

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Abstract

Semi-Dirac cones, a type of unique dispersion relation, always exhibit a series of interesting transport properties, such as electromagnetic topological transitions and anisotropic electromagnetic transmission. Recently, dual-band semi-Dirac cones have been found in three-dimensional photonic crystals, presenting great potential in electromagnetic wave regulation. However, to the best of our knowledge, there has been no report on dual-band semi-Dirac cones and their applications in two-dimensional photonic crystals, and most of two-dimensional systems have only realized semi-Dirac cones at a single frequency. Therefore, we are to realize dual-band semi-Dirac cones in two-dimensional photonic crystals. In this work, a type of two-dimensional photonic crystal that comprises a square lattice of elliptical cylinders embedded in air is proposed. By rotating the elliptical cylinders and adjusting their sizes appropriately, accidental degeneracy at two different frequencies is achieved simultaneously in the center of the Brillouin zone. Using ${\boldsymbol{k}} \cdot {\boldsymbol{p}}$ perturbation theory, the dispersion relations near the two degenerate points are proved to be nonlinear in one direction, and linear in other directions. These results indicate that the double accidental degenerate points are two semi-Dirac points with different frequencies, and two different semi-Dirac cones, i.e. dual-band semi-Dirac cones, are realized simultaneously in our designed photonic crystal. More interestingly, the dual-band semi-Dirac cones exhibit opposite linear and nonlinear dispersion relation along the major axis and the minor axis of the ellipse, respectively. And our photonic crystal can be equivalent to an impedance-matched double-zero index material in the direction of linear dispersion and a single-zero index material in the direction of nonlinear dispersion, which is demonstrated by the perfect transmission in the straight waveguide and wavefront shaping capabilities of electromagnetic waves. Based on the different properties of the equivalent zero-refractive-indices near the frequencies of two semi-Dirac point, the designed Y-type waveguide can be used to realize frequency separation by leading out the plane waves of different frequencies along different ports. We believe that our work is meaningful in broadening the exploration of the band structures of two-dimensional photonic crystals and providing greater convenience for regulating electromagnetic waves.

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作者及机构信息

通信作者:李妍,liyanQFNU@163.com

基金项目:山东省自然科学基金青年科学基金(批准号: ZR2016AQ09)和国家自然科学基金青年科学基金(批准号: 11704219)资助的课题.

Authors and contacts

Corresponding author:Li Yan,liyanQFNU@163.com

Funds:Project supported by the Young Scientists Fund of the Natural Science Foundation of Shandong Province, China (Grant No. ZR2016AQ09) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11704219).

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施引文献

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