半导体微盘谐振腔的模式特性研究
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摘要
半导体微腔激光器由于其高集成度、低阈值、低功耗等优点而在通信、光互联和光神经网络等方面有着广阔的应用前景,并且作为最早发展起来的微腔激光器,已引起研究者广泛的关注。
半导体激光器的数值分析是器件制作的基础,本文分别运用解析法和时域有限差分方法对二维圆形微腔和三维圆盘微腔进行了数值模拟,并考察了它们的模式特性。
通过计算得出的主要结果如下:
一、运用解析法分析了二维圆盘微腔的模式特性。对空气中的折射率为n_1=2.56的圆盘,我们给出了TE模式波长随角量子数v和径向量子数l的变化。图中可以看出,随着径向量子数l和角量子数v的增加,模场分布更趋向于限制在圆内。
二、运用三维时域有限差分(FDTD)方法,用FullWAVE软件为辅助,讨论了纵向折射率分布为n_(air)/3.4/n_(sub)的圆盘结构的模式特性,其中,空气折射率n_(air)=1.0。当衬底折射率n_(sub)由2.0变化到3.17时,对于半径为1μm,厚度为0.2μm的对称盘,我们用时域有限差分方法得到了横模和纵模图,从这些横模图我们可以得到关于半导体微盘激光器的模式特性的一些结论。从图中可以看出微腔中的主要光学模式是一种沿着边缘进行环状传播的具有较高品质因子的特殊模式—“回音壁”模式(Whisper Gallery Mode)。当衬底折射率小时,由于在有源区与衬底的边界处光波被全反射,所以光波被限制在折射率大的有源层内,沿着有源层面的方向传播。当衬底折射率接近有源区折射率时有明显的光泄露。
三、运用FDTD方法对半径为1μm,厚度为0.2μm,纵向折射率分布为n_(air)/3.4/n_(sub)的圆盘微腔进行光场分布模拟时发现,当衬底折射率n_(sub)由2.0变化到3.17时,圆盘横向基模和一阶模的模式波长的变化趋向于交叉耦合。进一步分析发现,当n_(sub)=2.0和2.5时两种模式的光在圆盘微腔横向和纵向方向上很好地被限制,光场分布都呈现出“回音壁”特点,若使在圆盘中形成“回音壁”模式特点的光场分布,则尽量要拉大圆盘和衬底折射率之差,当n_(sub)=2.8到3.17时两种模式的光在纵向方向上限制变弱,在衬底中光能量泄露明显增多,变化到n_(sub)=3.17时两种模式中TE_(01)模式逐渐偏离“回音壁”模式特点。另外比起低阶模式,高阶模式更容易形成“回音壁”模式。还有我们把第三章和第四章得到的光场分布结果进行了比较,结果发现,我们得到非常接近的结果。这对半导体微盘激光器的设计具有一定的理论指导意义。
Semiconductor microcavity laser has a lot of merit such as ultrasmall volumn、ultralow threshold current and so on,so it has great application potential in optical communication,optical interconnection and optical neural networks.As the earliest developed microcavity laser, Microdisk laser has attracted researchers' great attention all over the world.
It is known that the numerical value analysis of Semiconductor laser is the basis of devices production.In this thesis,2-dimensional(2-D) and 3-dimensional(3-D) microdisk lasers are analysed by using the Analytical Method and the Finite-Difference Time-Domain technique, (FDTD) and some important results are achieved as follows:
By using Analytical Method,the properties of the mode for the 2-dimensional(2-D) microdisk are investigated.As for the microdisk with the refractive index of n_1= 2.56 in the air,the TE mode's changes according to azimuthal quantum number v and radial mode number l is given.In addition,the mode field distributions tends to be limited within the circle with the increasing of the azimuthal mode number v and radial mode number l.
By using 3-D Finite-Difference Time-Domain technique as well as with the aid of FULLWAVE,the properties of the mode for the microdisk with a vertical refractive index distribution of n_(air)/3.4/n_(sub) are investigated.The map of TE mode and vertical mode is obtained by 3D-FDTD simulation for the microdisk with a thickness of 0.2μm,and a radius of 1μm,when the refractive index is n_(air)=1.0,the refractive index n_(sub) is varied from 2.0 to 3.17,from which we can obtain the conclusion about the mode properties of the microdisk laser.From the map we can find the main optical mode in the microcavity is a special mode-whisper Gallery Mode with high quality factor,transmitting circularly on the edge of microdisk.When the refractive index n_(sub) is minimums,because the light wave is fully reflected on the interface between the disk and the substrate,the light wave is limited within the disk,transmitting along the disk.corresponding to an increasing horizontal radiation loss,when refractive index n_(sub) is similar to active regions refractive index.
For the microdisk with a thickness of 0.2μm,a radius of 1μm and the vertical refractive index distribution of n_(air)/3.4/n_(sub),the two modes' wavelengths tend to be identical--a mode across coupling trend is observed between the fundamental and the first order modes when the refractive index n_(sub) change from 2.0 to 3.17.when n_(sub)=2.0,n_(sub)=2.5, the two modes are limited horizontally and vertically in Cylindrically microcavity--both of the Optical-Field Distribution will possess of quite good whispering-gallery modes characteristic,if wanting to get the Optical-Field Distribution with the whispering-gallery modes characteristic,we must try to magnify the difference.When n_(sub)=2.8,n_(sub)=3.17,the vertical limit to the option is decling--the loss of the optical energy is obviously increasing at the substrate,and when n_(sub)=3.17,the TE_(01) mode gradually deviates from the features of the whispering-gallery modes.Furthermore,compared with fundamental mode,high mode is much easier to form the whispering-gallery modes. The results of the optical field distribution in chapter 3 and chapter 4 are compared only to find the quite close results.The above-mentioned conclusions will have a practical significance to the design of the semiconductor microcavity lasers.
半导体激光器的数值分析是器件制作的基础,本文分别运用解析法和时域有限差分方法对二维圆形微腔和三维圆盘微腔进行了数值模拟,并考察了它们的模式特性。
通过计算得出的主要结果如下:
一、运用解析法分析了二维圆盘微腔的模式特性。对空气中的折射率为n_1=2.56的圆盘,我们给出了TE模式波长随角量子数v和径向量子数l的变化。图中可以看出,随着径向量子数l和角量子数v的增加,模场分布更趋向于限制在圆内。
二、运用三维时域有限差分(FDTD)方法,用FullWAVE软件为辅助,讨论了纵向折射率分布为n_(air)/3.4/n_(sub)的圆盘结构的模式特性,其中,空气折射率n_(air)=1.0。当衬底折射率n_(sub)由2.0变化到3.17时,对于半径为1μm,厚度为0.2μm的对称盘,我们用时域有限差分方法得到了横模和纵模图,从这些横模图我们可以得到关于半导体微盘激光器的模式特性的一些结论。从图中可以看出微腔中的主要光学模式是一种沿着边缘进行环状传播的具有较高品质因子的特殊模式—“回音壁”模式(Whisper Gallery Mode)。当衬底折射率小时,由于在有源区与衬底的边界处光波被全反射,所以光波被限制在折射率大的有源层内,沿着有源层面的方向传播。当衬底折射率接近有源区折射率时有明显的光泄露。
三、运用FDTD方法对半径为1μm,厚度为0.2μm,纵向折射率分布为n_(air)/3.4/n_(sub)的圆盘微腔进行光场分布模拟时发现,当衬底折射率n_(sub)由2.0变化到3.17时,圆盘横向基模和一阶模的模式波长的变化趋向于交叉耦合。进一步分析发现,当n_(sub)=2.0和2.5时两种模式的光在圆盘微腔横向和纵向方向上很好地被限制,光场分布都呈现出“回音壁”特点,若使在圆盘中形成“回音壁”模式特点的光场分布,则尽量要拉大圆盘和衬底折射率之差,当n_(sub)=2.8到3.17时两种模式的光在纵向方向上限制变弱,在衬底中光能量泄露明显增多,变化到n_(sub)=3.17时两种模式中TE_(01)模式逐渐偏离“回音壁”模式特点。另外比起低阶模式,高阶模式更容易形成“回音壁”模式。还有我们把第三章和第四章得到的光场分布结果进行了比较,结果发现,我们得到非常接近的结果。这对半导体微盘激光器的设计具有一定的理论指导意义。
Semiconductor microcavity laser has a lot of merit such as ultrasmall volumn、ultralow threshold current and so on,so it has great application potential in optical communication,optical interconnection and optical neural networks.As the earliest developed microcavity laser, Microdisk laser has attracted researchers' great attention all over the world.
It is known that the numerical value analysis of Semiconductor laser is the basis of devices production.In this thesis,2-dimensional(2-D) and 3-dimensional(3-D) microdisk lasers are analysed by using the Analytical Method and the Finite-Difference Time-Domain technique, (FDTD) and some important results are achieved as follows:
By using Analytical Method,the properties of the mode for the 2-dimensional(2-D) microdisk are investigated.As for the microdisk with the refractive index of n_1= 2.56 in the air,the TE mode's changes according to azimuthal quantum number v and radial mode number l is given.In addition,the mode field distributions tends to be limited within the circle with the increasing of the azimuthal mode number v and radial mode number l.
By using 3-D Finite-Difference Time-Domain technique as well as with the aid of FULLWAVE,the properties of the mode for the microdisk with a vertical refractive index distribution of n_(air)/3.4/n_(sub) are investigated.The map of TE mode and vertical mode is obtained by 3D-FDTD simulation for the microdisk with a thickness of 0.2μm,and a radius of 1μm,when the refractive index is n_(air)=1.0,the refractive index n_(sub) is varied from 2.0 to 3.17,from which we can obtain the conclusion about the mode properties of the microdisk laser.From the map we can find the main optical mode in the microcavity is a special mode-whisper Gallery Mode with high quality factor,transmitting circularly on the edge of microdisk.When the refractive index n_(sub) is minimums,because the light wave is fully reflected on the interface between the disk and the substrate,the light wave is limited within the disk,transmitting along the disk.corresponding to an increasing horizontal radiation loss,when refractive index n_(sub) is similar to active regions refractive index.
For the microdisk with a thickness of 0.2μm,a radius of 1μm and the vertical refractive index distribution of n_(air)/3.4/n_(sub),the two modes' wavelengths tend to be identical--a mode across coupling trend is observed between the fundamental and the first order modes when the refractive index n_(sub) change from 2.0 to 3.17.when n_(sub)=2.0,n_(sub)=2.5, the two modes are limited horizontally and vertically in Cylindrically microcavity--both of the Optical-Field Distribution will possess of quite good whispering-gallery modes characteristic,if wanting to get the Optical-Field Distribution with the whispering-gallery modes characteristic,we must try to magnify the difference.When n_(sub)=2.8,n_(sub)=3.17,the vertical limit to the option is decling--the loss of the optical energy is obviously increasing at the substrate,and when n_(sub)=3.17,the TE_(01) mode gradually deviates from the features of the whispering-gallery modes.Furthermore,compared with fundamental mode,high mode is much easier to form the whispering-gallery modes. The results of the optical field distribution in chapter 3 and chapter 4 are compared only to find the quite close results.The above-mentioned conclusions will have a practical significance to the design of the semiconductor microcavity lasers.
引文
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