二维空气环型光子晶体的带隙及负折射特性研究
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摘要
光子晶体是介电常数在空间呈周期性排列形成的人工结构。光子带隙是光子晶体的重要特征之一,也是光子晶体应用研究的基础。因此,对光子晶体禁带特性的研究是光子晶体研究的重要内容。同时,电磁波在光子晶体中的负折射现象也引起了人们的广泛关注。本文重点研究了二维三角晶格空气环型光子晶体的能带及负折射特性,并基于负折射成像的原理设计了一种新型的点光源分光器。
采用平面波展开法(PWE)计算并分析了不同材料(GaAs、Si、Ge)组成的二维三角晶格空气孔、空气环型光子晶体的带隙结构,并就结构参数对光子晶体完全带隙的影响做了详细讨论。研究结果表明,材料介电常数越大两种结构得到的完全带隙越宽;由锗(Ge)作为背景材料的空气环型光子晶体的完全带隙比空气孔型结构增宽了66%。
研究了由空气环结构组成的二维三角晶格光子晶体平板的负折射特性。通过有效折射率的计算,得到了有效折射率为-1的电磁波频率随空气环内径变化的关系;借助对等频率曲线的分析,发现外径为R=0.40α,内径r为0～0.13a的空气环型结构,归一化频率为0.30的等频率曲线始终保持为圆形,可以实现较好的成像。采用时域有限差分法(FDTD)模拟了光子晶体平板的成像及线光源的负折射传输过程,模拟结果很好地证实了由平面波展开法计算得到的结论。
基于光子晶体的负折射原理,设计了一种新型分光器结构,解决了点光源的分光问题,设计了三角、六角两个不同的分光模型,并对每个模型的分光性能进行了对比分析,得到了较为理想的结构参数。
Photonic crystal is a kind of manufactured material with periodic arrangement of dielectric constant. Photonic band gap structure of photonic crystal indicates its primary property, which is the base of its design and application. The study on photonic band gap structure is an important part of basic research on photonic crystal. At the same time, negative refraction of electromagnetic waves in photonic crystal has attracted much attention because of variety of novel phenomena. In this paper, some research has been done on the photonic band gap and negative refraction of a novel two-dimensional photonic crystal, which is arranged in triangular lattice with ring-shaped air holes.
Photonic band gap structures of two-dimensional photonic crystal in triangular lattice with circular/ring-shaped air holes have been calculated by the plane wave expansion method (PWE). Three kinds of dielectric material (Si, GaAs, Ge) have been chosen as background in order to analysis the effects of the dielectric constant to band structure. The effects of parameters of the structure to band structure have been also analyzed. The results show that the structure composed of higher dielectric constant material has larger photonic band gap, and photonic band gap of the ring-shaped structure composed of Ge is 66% larger than that of the circular one.
Negative refraction in two-dimensional photonic crystal with ring-shaped holes is studied in detail. By the calculation of effective index, the relationship between inner radius and the frequencies with n_(eff)=-1 is obtained. The results show that the equal-frequency contour is a circle, so a perfect image can be obtained with the increasing of inner radius of ring-shaped holes from 0 to 0.13a and the outside radius 0.40a at normalized frequency 0.30. The simulation by the finite-difference time-domain method (FDTD) verifies the result calculated by PWE method.
Based on the principle of negative refraction in photonic crystal, a new type of splitter which can work well with point light source is designed. There are two models put forward in this paper, one is triangular and the other is hexagonal. By the analysis of performance of splitter more ideal structure parameters have been obtained.
采用平面波展开法(PWE)计算并分析了不同材料(GaAs、Si、Ge)组成的二维三角晶格空气孔、空气环型光子晶体的带隙结构,并就结构参数对光子晶体完全带隙的影响做了详细讨论。研究结果表明,材料介电常数越大两种结构得到的完全带隙越宽;由锗(Ge)作为背景材料的空气环型光子晶体的完全带隙比空气孔型结构增宽了66%。
研究了由空气环结构组成的二维三角晶格光子晶体平板的负折射特性。通过有效折射率的计算,得到了有效折射率为-1的电磁波频率随空气环内径变化的关系;借助对等频率曲线的分析,发现外径为R=0.40α,内径r为0～0.13a的空气环型结构,归一化频率为0.30的等频率曲线始终保持为圆形,可以实现较好的成像。采用时域有限差分法(FDTD)模拟了光子晶体平板的成像及线光源的负折射传输过程,模拟结果很好地证实了由平面波展开法计算得到的结论。
基于光子晶体的负折射原理,设计了一种新型分光器结构,解决了点光源的分光问题,设计了三角、六角两个不同的分光模型,并对每个模型的分光性能进行了对比分析,得到了较为理想的结构参数。
Photonic crystal is a kind of manufactured material with periodic arrangement of dielectric constant. Photonic band gap structure of photonic crystal indicates its primary property, which is the base of its design and application. The study on photonic band gap structure is an important part of basic research on photonic crystal. At the same time, negative refraction of electromagnetic waves in photonic crystal has attracted much attention because of variety of novel phenomena. In this paper, some research has been done on the photonic band gap and negative refraction of a novel two-dimensional photonic crystal, which is arranged in triangular lattice with ring-shaped air holes.
Photonic band gap structures of two-dimensional photonic crystal in triangular lattice with circular/ring-shaped air holes have been calculated by the plane wave expansion method (PWE). Three kinds of dielectric material (Si, GaAs, Ge) have been chosen as background in order to analysis the effects of the dielectric constant to band structure. The effects of parameters of the structure to band structure have been also analyzed. The results show that the structure composed of higher dielectric constant material has larger photonic band gap, and photonic band gap of the ring-shaped structure composed of Ge is 66% larger than that of the circular one.
Negative refraction in two-dimensional photonic crystal with ring-shaped holes is studied in detail. By the calculation of effective index, the relationship between inner radius and the frequencies with n_(eff)=-1 is obtained. The results show that the equal-frequency contour is a circle, so a perfect image can be obtained with the increasing of inner radius of ring-shaped holes from 0 to 0.13a and the outside radius 0.40a at normalized frequency 0.30. The simulation by the finite-difference time-domain method (FDTD) verifies the result calculated by PWE method.
Based on the principle of negative refraction in photonic crystal, a new type of splitter which can work well with point light source is designed. There are two models put forward in this paper, one is triangular and the other is hexagonal. By the analysis of performance of splitter more ideal structure parameters have been obtained.
引文
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