毕业设计（论文）-ZnO纳米柱无序介质中泵浦面积对局域模发射的影响.doc

存档编号赣南师范学院学士学位论文ZnO纳米柱无序介质中泵浦面积对局域模发射的影响教学学院物理与电子信息学院届别2011专业物理学学号姓名指导教师完成日期2011.5目录内容摘要···················································································1关键词······················································································1Abstract···················································································1Keyword···················································································11FDTD法的基本原理··································································21.1Maxwell方程及其FDTD形式··················································21.2FDTD的稳定性件··································································51.3PML吸收边界条件·································································61.4激励源的设置······································································72ZnO纳米柱无序介质的结构模型和增益模型·································73数值模拟················································································83.1频谱特性和光场分布······························································93.2泵浦面积对局域模激发特性的影响·········································104结论与讨论············································································14参考文献··················································································16致谢·························································································171ZnO纳米柱无序介质中泵浦面积对局域模发射的影响摘要：基于ZnO纳米柱制备及发光实验，本文建立ZnO纳米柱的位置和大小都是无序的二维介质结构模型，研究了无序介质中频谱特性和局域模的光场分布情况。除此之外，还分了以下几种情况研究泵浦面积对局域模激发特性的影响：改变泵浦功率从左到右依次增加两层ZnO纳米柱泵浦和单独泵浦一个局域区域；泵浦功率一定时，增加泵浦局域区域和非局域区域中ZnO纳米柱个数。得到当泵浦功率较小时，无论泵浦面积多大都不能激发局域模；不同的泵浦功率，局域模被激发所需的临界泵浦面积不同。随着泵浦功率增加，光场相对强度呈递增趋势，泵浦面积不同时，被激发的局域模也不同。而泵浦非局域区域，光场分布没什么变化的结论。关键词：无序介质局域模泵浦面积受激辐射Abstract:BasedonthegrowthandphotoluminescenceexperimentofZnOnanorods,thestructuralmodeloftwo-dimensionalrandommediainwhichthecenterandradiusofZnOnanorodsarealldisorderedisconstructed,UsingZnOgainphenomenologicalmodel,thespectrumcharacteristicsandspatialdistributionofopticalfieldatsomeresonantpeakinZnOnanorodsrandommediaaresimulatednumericallybymeansofthefinitedifferencetimedomainmethod,thelocalizedmodeisfound.TheeffectofpumpareaonlaseractionsinZnOnanorodsrandommediawasstudiedfromfollowingaspects,changethepumpintensity,increasingthepumpsizeeverytwocolumnsfromlefttorightandonlypumpazoneoflocalizedmode.Thepumpintensityisfixed,increasingtheexcitationarea(thenumberoftheZnOnanorods)inlocalizedareaandnon-localarearespectively.TheresultgivesussomeinformationaboutthedependenceofrandomlaseractionsonpumpareainZnOnanorodsactiverandommedia.Keywords:randommedialocalizedmodepumpsizesstimulatedemission21968年Letokhov首次计算了增益介质中无序光放大和光散射现象1。ZnO是理想的强散射和高增益的材料，并有很大的能隙，室温下带隙宽度为3.37ev和激子束缚能高达60mev，使得高温下激光器低阈值的实用前景成为可能2。ZnO无序介质的发光特性引起了人们的广泛关注，H.CaO等人先后制备出粉末、薄膜、团簇、纳米柱多种形态ZnO材料，并在其上观察到了激光辐射现象3-7。高密度ZnO纳米柱阵列中，如果相应增益长度和散射平均自由程满足形成激光的要求则能形成无序激光，在ZnO纳米柱阵列中观察到了相干反馈无序激光行为,研究已发现ZnO纳米柱阵列中阈值泵浦强度与泵浦体积有关6、8。2003年，H.Cao工作组利用了等离子增强蒸汽沉积的方法，在实验室中成功制备出了直径在20-75nm范围内的ZnO纳米柱7，并测试了其光学特性，但对ZnO纳米柱的发光特性的影响尚未见详细报道。本文将在H.Cao工作组开展的ZnO纳米柱制备及发光实验基础上，利用时域有限差分法9进一步探讨ZnO纳米柱中泵浦面积对局域模激发特性的影响。1FDTD法的基本原理FDTD（FiniteDifferenceTimeDomain)方法是直接对于Maxwell方程组求解，并且除了在时间和空间上的数值离散处理以外，没有采用任何物理上的近似，这表明了FDTD方法在理论上是一个非常精确的方法.迄今为止,FDTD法作为最为基本的模拟方法被研究工作大量地使用。主要的原因是FDTD无任何理论近似，研究范畴不受结构和材料的限制,并随着计算机运算能力大幅提升，促进了利用FDTD的相关研究。1.1Maxwell方程及其FDTD形式3在二维的情况下，假设所有的物理量均与z坐标无关，于是电磁波可以分成两种模式：TE波和TM波。其中TE波中只含有EX,EY和HZ分量，而TM波中只含有HX,HY和EZ分量，于是两种模式的Maxwell方程组分别可以写为：zmzxyyyzxxzHtHyExEEtExHEtEyHTE波(1.1.1)zzxyymyzxmxzEtHyHxHHtExEHtHyETM波(1.1.2)二维Yee元胞中E、H各分量节点取样如图1所示，对于TE波，HX=HY=EZ=0,方程(1.1.1)可以离散成如下形式1121212,12,12,1212,12nnxaxnnzzbEijCmEijHijHijCmy(1.1.3)11212,12,1212,1212,12nnyaynnzzbEijCmEijHijHijCmx(1.1.4)121212,1212,121,12,1212,112,zaznnyybnnxxHijDmHijEijEijDmxEijEijy(1.1.5)4图1二维TE和TM波Yee元胞电场和磁场分量，其中左TE波右TM波对于TM波，EX=EY=HZ离散为如下形式1212,1,12,12nnzznnxaxbEijEijHijDmHijDmy(1.1.6)12121,12,12,nnzznnyaybEijEijHijDmHijDmx(1.1.7)12121121212,12,12,12nnyynnzazbnnxxHijHijEijCmEijCmxHijHijy(1.1.8)m的取值与左端场分量节点的空间位置相同。其中122122amtmmmtCmmmmttm51122btmCmmmmttm122122mmammmtmmmtDmmmmttm1122bmmtmDmmmmttm(1.1.9)1.2FDTD的稳定性条件由于FDTD方法特点是用一组有限差分方程来代替Maxwell旋度方程，因此差分方程组的解必须是收敛的和稳定的。即当离散间隔趋于零时，在空间任意一点和任意时刻这些差分方程的解都会一致趋于它原方程的解，并且它们的数值解与原方程的严格解之差是有界的。因此在离散过程中时间间隔和空间网格间距都必须符合相应的要求。(1)时间稳定性条件。在FDTD方法中，时间稳定性条件即时间间隔和空间间隔之间需要满足的关系，它的数学表达式为2221111tcxyz(1.2.1)在正方网格的情况下，由于x=y=z,上式可以写为33xtc(1.2.2)上式可理解为时间间隔不能大于光穿过空间网格对角线时间的1/3。如