Band Structure of One-dimensional Photonic Crystal with Dielectric Constant as a Sine-squared Function in Coordinate Space

LI Hong-tao; SHAO Ming-zhu; LUO Shi-yu

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Band Structure of One-dimensional Photonic Crystal with Dielectric Constant as a Sine-squared Function in Coordinate Space

更新时间：2020-08-12

- Band Structure of One-dimensional Photonic Crystal with Dielectric Constant as a Sine-squared Function in Coordinate Space
- Chinese Journal of Luminescence Vol. 29, Issue 2, Pages: 229-232(2008)
- 作者机构：
  
  东莞理工学院,广东东莞,523106
- 作者简介：
- 基金信息：
- DOI：
  CLC： O437;O431.1
- Received：25 August 2007，
  
  Revised：24 November 2007，
  
  Published：20 March 2008
- 稿件说明：
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李洪涛, 邵明珠, 罗诗裕. 介电常数呈正弦平方规律变化的一维光子晶体带结构[J]. 发光学报, 2008,29(2): 229-232

LI Hong-tao, SHAO Ming-zhu, LUO Shi-yu. Band Structure of One-dimensional Photonic Crystal with Dielectric Constant as a Sine-squared Function in Coordinate Space[J]. Chinese Journal of Luminescence, 2008,29(2): 229-232
李洪涛, 邵明珠, 罗诗裕. 介电常数呈正弦平方规律变化的一维光子晶体带结构[J]. 发光学报, 2008,29(2): 229-232 DOI：

LI Hong-tao, SHAO Ming-zhu, LUO Shi-yu. Band Structure of One-dimensional Photonic Crystal with Dielectric Constant as a Sine-squared Function in Coordinate Space[J]. Chinese Journal of Luminescence, 2008,29(2): 229-232 DOI：

摘要

一维光子晶体是最简单的一类光子晶体。利用分子束外延生长技术

人们可以把两种折射率(或介电常数)不同的材料交替生长形成多层薄膜结构。由于对称性

人们就把这种多层薄膜材料近似当作一维光子晶体

并研究不同折射率情况下光子晶体的能带特征。假设介电常数呈正弦平方规律变化

光子的运动方程化为熟知的Mathieu方程。根据Bloch定理讨论了系统的能量分布

系统自动呈现出的能带结构

再现了光子晶体的周期性与能带特征。数值分析表明

在参数(δ

ε)平面上系统出现了一系列稳定和不稳定区(禁带)。当参数|ε|→0时

这些不稳定区退化为一点

给出了禁带中心频率

并用摄动法求解了方程的低阶不稳定区及其禁带宽度。结果表明

一阶和二阶不稳定区(禁带)宽度Δω

与介质的参数和入射光子频率有关。适当选择这些参数

可以有效地调节光子晶体的带结构

并按需要得到不同性能的光子晶体。

Abstract

Photonic crystals are artificially created materials with periodic dielectric constant variations. The simplest one-dimensional photonic crystals are multilayer structures obtained by alternately growing thin-films with different dielectric constants by molecular beam epitaxy. When the dielectric constant of one-dimensional photonic crystal is a sine-squared function in coordinate space

the photonic motion equation is reduced to Mathieu equation.The band construction for this system is discussed based on Bloch theorem

and the system presented automatically band properties.It shows that there are a series of stable zones and unstable zones (forbidden-bands) in the plane of parameter δ and ε. When |ε|→>0

these unstable zones will be reduced to some points in the centre of the forbidden-bands. The unstable zone and the forbidden-band width are found by the perturbation techniques.The result shows that the widths of the first order and second order unstable zones depend on the parameters of dielectric and photonic frequency. By adjusting these parameters

one can obtain the photonic crystals with different band structures and properties.

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references

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Chen Song,Wang Weibiao,Liang Jingqiu,et al.Two-dimensional square photonic crystal microcavity[J].Chin.J.Lumin.(发光学报),2007,28(1):7-12 (in Chinese).

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Chen Weizong,Hu Manli,Li Shaoxiong,et al.Character and widness of forbidden band of one-dimensional photonic crystal[J].J.Northwest University (Natural Science Edition)(西北大学学报(自然科学版)),2002,32(6):625-628 (in Chinese).

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