摘要
光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.
Photonic crystal is a kind of periodic optical nanostructure consisting of two or more materials with different dielectric constants, which has attracted great deal of attention because of its wide range of potential applications in the field of optics. Photonic crystal can be fabricated into one-, or two-, or three-dimensional one. Among them, the two-dimensional photonic crystal turns into a hot focus due to its fantastic optical and electrical properties and relatively simple fabrication technique. Since the tunable band gaps of two-dimensional photonic crystals are beneficial to designing the novel optical devices, to study their optical and electrical properties for controlling the electromagnetic wave is quite valuable in both theoretical and practical aspects. In this work, we propose a new type of two-dimensional function photonic crystal, which can tune the band gaps of photonic crystals. The two-dimensional function photonic crystal is different from the traditional photonic crystal composed of medium columns with spatially invariant dielectric constants,since the dielectric constants of medium column are the functions of space coordinates. Specifically, the photorefractive nonlinear optical effect or electro-optic effect is utilized to turn the dielectric constant of medium column into the function of space coordinates, which results in the formation of two-dimensional function photonic crystal. We use the plane-wave expansion method to derive the eigen-equations for the TE and TM mode. By the Fourier transform, we obtain the Fourier transform form ε（G） for the dielectric constant function ε（r） of two-dimensional function photonic crystal, which is more complicated than the Fourier transform in traditional two-dimensional photonic crystal. The calculation results indicate that when the dielectric constant of medium column is a constant, the Fourier transforms for both of them are the same, which implies that the traditional two-dimensional photonic crystal is a special case for the two-dimens
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2016年第13期154-162,共9页
Acta Physica Sinica
基金
吉林省科技发展计划项目(批准号:20130101031JC)资助的课题~~
关键词
二维函数光子晶体
平面波展开法
带隙结构
two-dimensional function photonic crystals
plane wave expansion
band gap structure
