无序光子晶体中半定域Anderson模的产生
Emergence of semi-localized Anderson modes in a disordered photonic crystal as a result of overlap probability
摘要：
本文研究了位置随机性对二维光子晶体透射特性的影响，它是随机性参数$α$（$α=0$完全有序，$α=1$完全无序）的函数。本文采用时域有限差分法（FDTD）数值求解了这种介质中的麦克斯韦方程组。我们考虑了两种情况：第一种是$90\degr$弯曲光子晶体波导，第二种是中心脉冲光子晶体微腔。我们为每种情况绘制了各种数字，这些数字定量地描述了随机性的影响。更具体地说，在波导的情况下，我们表明，一般形状的归一化总输出能量是一个高斯函数的随机性与波长相关的宽度。对于中心脉冲PC，输出能量曲线显示极值行为作为时间的函数以及随机性。我们解释这些影响方面的两个不同的，但同时出现的随机性增加，即创建半本地化模式和收缩（并最终破坏）的光子带隙。半本地化（即安德森本地化）模式被视为出现作为一个随机定位的介电纳米粒子的集群内的内部模式的同步。我们观察到的总体趋势显示了中间随机度区域（即$α\approx 0.5$）中行为的急剧变化，我们将其归因于纳米颗粒的潜在重叠概率中的类似行为
英文摘要：
In this paper we study the effect of positional randomness on transmissional properties of a two dimensional photonic crystal as a function of a randomness parameter $α$ ($α=0$ completely ordered, $α=1$ completely disordered). We use finite-difference time-domain~(FDTD) method to solve the Maxwell's equations in such a medium numerically. We consider two situations: first a $90\degr$ bent photonic crystal wave-guide and second a centrally pulsed photonic crystal micro-cavity. We plot various figures for each case which characterize the effect of randomness quantitatively. More specifically, in the wave-guide situation, we show that the general shape of the normalized total output energy is a Gaussian function of randomness with wavelength-dependent width. For centrally pulsed PC, the output energy curves display extremum behavior both as a function of time as well as randomness. We explain these effects in terms of two distinct but simultaneous effects which emerge with increasing randomness, namely the creation of semi-localized modes and the shrinking (and eventual destruction) of the photonic band-gaps. Semi-localized (i.e. Anderson localized) modes are seen to arise as a synchronization of internal modes within a cluster of randomly positioned dielectric nano-particles. The general trend we observe shows a sharp change of behavior in the intermediate randomness regime (i.e. $α\approx 0.5$) which we attribute to a similar behavior in the underlying overlap probability of nano-particles
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