光子晶体多组元缺陷态问题研究

摘要/Abstract

摘要： 缺陷态光子晶体可以用于制作良好的谐振器、偏振器、滤光器等光学器件,具有重要的应用价值。本文发展了光子晶体缺陷态问题的PG有限元界面问题计算方法,有效地处理了各种不同组元体系、几何结构、界面形状、材料属性以及模态的光子晶体缺陷态问题。数值结果表明,二组元结构单点缺陷对带隙的影响较小,只是使局部范围内的波继续传播而产生一条缺陷带,多点缺陷使一些特定范围内的波可以传播而产生多条缺陷带,线缺陷产生的影响较大,可以使整个禁带消失。结合线缺陷与点缺陷,波导结构中的侧点缺陷可以有效地应用于光子晶体阻带内诱导窄通带或在波导的通带内诱导非常窄的阻带。三组元结构引入了不均匀介质、复杂介质形状以及不同几何结构的缺陷态。通过计算与分析发现Ω₃区域的介质形状对结果影响比较有限,表面层越不光滑禁带越窄,n型缺陷态在TM模中的高频区域更容易产生禁带。对于TE模来说,n型与v型的缺陷态更容易产生禁带。

关键词: 光子晶体, 缺陷态, 多组元, 能带结构, PG有限元法, 非贴体网格

Abstract: The defective photonic crystals have wide applications. They can often be used to make optical devices such as resonators, polarizers, and filters. In this paper, the Petrov-Galerkin finite element interface method is proposed to calculate the band structures of multi-component defective photonic crystals, the defect states of photonic crystals with different component systems, geometric structures, interface shapes, material properties and modes were effectively studied. Numerical results show that the single point defect of two-component structure has little influence on the band gap, which only makes the waves continue to propagate in the local range, resulting in a defect band, while the multiple point defect makes the waves in a certain range propagate and multiple defect bands are generated. On the other hand, the line defect has a great influence, which makes the whole forbidden band disappear. When line defects are combined with point defects, the lateral point defects in waveguide structures can be advantageously used to induce narrow passbands within the stopband of photonic crystals or to induce narrow stopbands within the passband of waveguides. The three-component structure introduces inhomogeneous media, complex media shapes and different geometry structures. It is noticed that the media shape in the Ω₃ region has limited influence on the results. The less smooth the surface layer is, the narrower the band gap is, and the high-frequency region in the TM mode of the n-type defect state is more likely to generate a band gap. For the TE mode, the n-type and v-type defect states are more likely to generate band gaps.

Key words: photonic crystal, defective state, multi-component, energy band structure, Petrov-Galerkin finite element method, non-body-fitted grid

中图分类号:

王立群, 严佳新, 卢欣, 石丽伟, 张肖利. 光子晶体多组元缺陷态问题研究[J]. 人工晶体学报, 2022, 51(6): 986-995.

WANG Liqun, YAN Jiaxin, LU Xin, SHI Liwei, ZHANG Xiaoli. Multi-Component Defect State of Photonic Crystals[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(6): 986-995.

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