亚波长金属结构对光波异常传输的FDTD数值模拟研究
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摘要
自1998年T. W. Ebbesen等人在Nature期刊上首次报道了金属薄膜上亚波长孔径阵列的异常光学透射（EOT）现象以来，亚波长或纳米尺度范围内光波-物质作用物理问题和技术应用已引起了世界各国科学家们的极大兴趣，并快速发展成为了当前光学领域中的研究热点。尽管目前针对亚波长金属结构中出现奇特效应的物理机制仍然存在许多争议，但大量研究表明外部电磁场与金属表面自由电子相互作用形成的一种相干共振，即表面等离子体激元（SPP）的激发，在其中扮演着至关重要的角色。事实上，如何深刻理解和清楚地揭示金属微纳结构与光波作用的物理本质已成为目前该研究领域内的重要基础课题。因此，我们有必要进一步深入开展相关的理论研究，探索和发现其中的新现象、新效应和新原理，为未来新型纳米光子器件的设计与开发奠定研究基础。
本论文主要运用二维时域有限差分（FDTD）数值模拟方法，并基于自行编写的C语言计算程序，比较详细的研究了亚波长金属银膜上单狭缝结构在近红外光波照射下的多种新异物理现象，深入阐述了这些现象与亚波长结构参数之间的相互关联，并分析探讨了其中的物理起源。本论文的主要研究结果如下：
1.系统研究了金属亚波长单狭缝在TM偏振光照射下发生增强透射的物理过程及其不同截面上的光强分布情况。模拟结果表明透射率曲线随着狭缝厚度变化产生周期性的多峰振荡，而随狭缝宽度变化至多出现一个峰值。透射光中辐射波和表面波之间的能量分配与狭缝宽度密切相关。另外，我们发现随着缝宽的增大，狭缝内壁之间的耦合模强度逐渐减弱，其空间模式也变得不再均匀。
2.首次研究了金属单狭缝结构在空间离散化情况下的增强透射特性。计算结果发现通过合理设计和调整缝内刻槽参数（槽宽、槽深及其填充物折射率等），离散化狭缝透射率较光滑情况可以获得进一步提高（约十倍左右）或者被完全抑制掉，理论分析认为透射率提高的物理机制来源于各狭缝基本单元内激发的理想SPP基模共振，及其在狭缝基本单元之间的多次散射与耦合过程。这可以用来有效提高纳米光子器件中SPP波信号的传输距离。
3.仿真模拟了透射空间填充不同折射率介质时，金属亚波长单狭缝结构对光波透射的电磁场分布情况，首次发现了在高折射率透射空间情况下，透射光束在近场区域内的空间聚焦和准直现象，而且聚焦光束的横向宽度为亚波长量级。进一步的研究结果表明聚焦光束的特征参数如焦距和焦深等随着狭缝宽度、透射空间介电常数和入射光波长的增大而增大。该研究有望在纳米光刻、传感探测和超分辨显微等方面有重要应用价值。
4.针对亚波长金属单狭缝结构在高折射率透射空间内出现的近场光束聚焦行为，我们首次提出了基于金属表面散射的准柱面波（QCW）近场干涉及其次波辐射的理论解释，即从狭缝出射拐点处散射的准柱面波首先在端口区域相互干涉产生纳米量级周期性空间分布的强度条纹，然后它们再作为次波源向透射空间辐射电磁波并叠加形成光束聚焦的效果，理论预测和模拟实验结果取得了较好的吻合。这对于深刻认识亚波长金属结构与光波作用的基本原理具有重要意义。
Since the first discovery of extraordinary optical transmission (EOT) throughsubwavelength hole arrays on the metal films, which was reported by Ebbesen et al.on Nature in1998, the goal of understanding the physical issues about thelight-matter interactions in the scale of subwavelength and nano-meter has attractedenormous interest around the world, and sprung on the intense research activities andutilizing these phenomena, whose rapid development makes it become a researchhotspot in the current optical field. Although the underlying mechanisms of thesepeculiar phenomena are still in a controversy, numerous studies have confirmed thatsurface plasmon polaritons (SPP), being a coherent collective oscillation of freeelectrons on the metal surface excited by the incident electromagnetic waves, shouldplay significant roles during the optical transmission processes. Actually, how tocomprehensively understand and clearly reveal the relevant physical essences hasalready been an open question in this research field. Therefore, it is very necessary tofurther carry out theoretical studies to explore some new phenomena and new effects,and try to discover their new principles, which will be of benefit to the futuredevelopment of the new nano photonic devices and their optimal designing work.
In this thesis, we employ the finite-difference time-domain (FDTD) numericalsimulation method and the self-compiled calculation program with C computerlanguage to investigate physical properties of the optical transmission through a silversubwavelength slit structure illuminated by the infrared incident waves. And then weintensively elucidate the relationships of these phenomena with the structuralparameters. Finally their physical origins are discussed. The main contents and resultsof this thesis are given as follows:
1. The physical processes of EOT from a subwavelength metallic slit illuminated byan incident transverse-magnetic wave and the involved electromagnetic fielddistributions in different cross-sections of the slit are investigated thoroughly. The simulation results reveal that the transmission efficiency seems to periodicallyoscillate with multiple peaks when the slit depth is varied, but it tends to give no morethan one peak profiled tendency for the change of the slit width. The ratio of theoutput energy dispensing between the radiative and surface wave components isidentified to closely depend on the slit width. On the other hand, with increasing theslit width, the field coupling intensity in the slit is found to reduce with accompany ofthe degrading uniform distribution of the spatial mode.
2. We investigate the upgrade transmission properties of a spatially quantized singlesubwavelength metallic slit. We find for the first time that the optical transmittancewill be further increased about ten times or suppressed effectively to zero, when thesmooth slit is discretized into several unit components by inside placing transversegrooves with suitable geometrical parameters (such as the width, depth, and therefractive index of the filling). The theoretical analysis suggest that the formation offundamental plasmon resonances inside the slit units and their multiple scattering andmutual coupling processes play a dominant role for the observations. This kind of slitquantization method can be used to improve the propagation distance of SPP signalsin nano-photonic devices.
3. We simulate the electromagnetic field distributions of the transmission lightthrough a single subwavelength metallic slit when the output space is set as differentpermittivities, and found for the first time that the near-field beam focusing andcollimating effect especially in the cases of high permittivity and relatively large slitwidth. The available transverse full-width and half-magnitude (FWHM) value of thefocal spot can be compressed into the subwavelength scales. Moreover, our detailedinvestigations demonstrate that the characteristic parameters of the beam focusingspot (for example, the focal length and the focus depth) tends to increase with the slitwidth, output permittivity, and incident wavelength. This new finding will beexpected to have potential applications in nanolithography, sensing probe, andsuper-resolution microscopy.
4. In order to understand the physical origins of the near-field beam focusing of thesingle metallic subwavelength slit with the high permittivity of output space, wepropose a interference model of the quasi-cylindrical waves scattered by the metallicslit, with accompany of the secondary light sources radiation processes. According tothe theory, the quasi-cylindrical waves are firstly scattered from the slit exit corners,and then they have a spatial interference to form the periodic intensity fringes, whichcan be acted as the secondary light sources to thereafter reemit electromagnetic waveswith the phase coherence. And their subsequent spatial interference in the near-fieldregion finally leads to the beam focusing of the transmission light. The theoreticalpredictions agree well with the simulation results. We believe that this theoryprovides a new sight into the physical interaction of the subwavelength metallicstructures and incident light waves.
本论文主要运用二维时域有限差分（FDTD）数值模拟方法，并基于自行编写的C语言计算程序，比较详细的研究了亚波长金属银膜上单狭缝结构在近红外光波照射下的多种新异物理现象，深入阐述了这些现象与亚波长结构参数之间的相互关联，并分析探讨了其中的物理起源。本论文的主要研究结果如下：
1.系统研究了金属亚波长单狭缝在TM偏振光照射下发生增强透射的物理过程及其不同截面上的光强分布情况。模拟结果表明透射率曲线随着狭缝厚度变化产生周期性的多峰振荡，而随狭缝宽度变化至多出现一个峰值。透射光中辐射波和表面波之间的能量分配与狭缝宽度密切相关。另外，我们发现随着缝宽的增大，狭缝内壁之间的耦合模强度逐渐减弱，其空间模式也变得不再均匀。
2.首次研究了金属单狭缝结构在空间离散化情况下的增强透射特性。计算结果发现通过合理设计和调整缝内刻槽参数（槽宽、槽深及其填充物折射率等），离散化狭缝透射率较光滑情况可以获得进一步提高（约十倍左右）或者被完全抑制掉，理论分析认为透射率提高的物理机制来源于各狭缝基本单元内激发的理想SPP基模共振，及其在狭缝基本单元之间的多次散射与耦合过程。这可以用来有效提高纳米光子器件中SPP波信号的传输距离。
3.仿真模拟了透射空间填充不同折射率介质时，金属亚波长单狭缝结构对光波透射的电磁场分布情况，首次发现了在高折射率透射空间情况下，透射光束在近场区域内的空间聚焦和准直现象，而且聚焦光束的横向宽度为亚波长量级。进一步的研究结果表明聚焦光束的特征参数如焦距和焦深等随着狭缝宽度、透射空间介电常数和入射光波长的增大而增大。该研究有望在纳米光刻、传感探测和超分辨显微等方面有重要应用价值。
4.针对亚波长金属单狭缝结构在高折射率透射空间内出现的近场光束聚焦行为，我们首次提出了基于金属表面散射的准柱面波（QCW）近场干涉及其次波辐射的理论解释，即从狭缝出射拐点处散射的准柱面波首先在端口区域相互干涉产生纳米量级周期性空间分布的强度条纹，然后它们再作为次波源向透射空间辐射电磁波并叠加形成光束聚焦的效果，理论预测和模拟实验结果取得了较好的吻合。这对于深刻认识亚波长金属结构与光波作用的基本原理具有重要意义。
Since the first discovery of extraordinary optical transmission (EOT) throughsubwavelength hole arrays on the metal films, which was reported by Ebbesen et al.on Nature in1998, the goal of understanding the physical issues about thelight-matter interactions in the scale of subwavelength and nano-meter has attractedenormous interest around the world, and sprung on the intense research activities andutilizing these phenomena, whose rapid development makes it become a researchhotspot in the current optical field. Although the underlying mechanisms of thesepeculiar phenomena are still in a controversy, numerous studies have confirmed thatsurface plasmon polaritons (SPP), being a coherent collective oscillation of freeelectrons on the metal surface excited by the incident electromagnetic waves, shouldplay significant roles during the optical transmission processes. Actually, how tocomprehensively understand and clearly reveal the relevant physical essences hasalready been an open question in this research field. Therefore, it is very necessary tofurther carry out theoretical studies to explore some new phenomena and new effects,and try to discover their new principles, which will be of benefit to the futuredevelopment of the new nano photonic devices and their optimal designing work.
In this thesis, we employ the finite-difference time-domain (FDTD) numericalsimulation method and the self-compiled calculation program with C computerlanguage to investigate physical properties of the optical transmission through a silversubwavelength slit structure illuminated by the infrared incident waves. And then weintensively elucidate the relationships of these phenomena with the structuralparameters. Finally their physical origins are discussed. The main contents and resultsof this thesis are given as follows:
1. The physical processes of EOT from a subwavelength metallic slit illuminated byan incident transverse-magnetic wave and the involved electromagnetic fielddistributions in different cross-sections of the slit are investigated thoroughly. The simulation results reveal that the transmission efficiency seems to periodicallyoscillate with multiple peaks when the slit depth is varied, but it tends to give no morethan one peak profiled tendency for the change of the slit width. The ratio of theoutput energy dispensing between the radiative and surface wave components isidentified to closely depend on the slit width. On the other hand, with increasing theslit width, the field coupling intensity in the slit is found to reduce with accompany ofthe degrading uniform distribution of the spatial mode.
2. We investigate the upgrade transmission properties of a spatially quantized singlesubwavelength metallic slit. We find for the first time that the optical transmittancewill be further increased about ten times or suppressed effectively to zero, when thesmooth slit is discretized into several unit components by inside placing transversegrooves with suitable geometrical parameters (such as the width, depth, and therefractive index of the filling). The theoretical analysis suggest that the formation offundamental plasmon resonances inside the slit units and their multiple scattering andmutual coupling processes play a dominant role for the observations. This kind of slitquantization method can be used to improve the propagation distance of SPP signalsin nano-photonic devices.
3. We simulate the electromagnetic field distributions of the transmission lightthrough a single subwavelength metallic slit when the output space is set as differentpermittivities, and found for the first time that the near-field beam focusing andcollimating effect especially in the cases of high permittivity and relatively large slitwidth. The available transverse full-width and half-magnitude (FWHM) value of thefocal spot can be compressed into the subwavelength scales. Moreover, our detailedinvestigations demonstrate that the characteristic parameters of the beam focusingspot (for example, the focal length and the focus depth) tends to increase with the slitwidth, output permittivity, and incident wavelength. This new finding will beexpected to have potential applications in nanolithography, sensing probe, andsuper-resolution microscopy.
4. In order to understand the physical origins of the near-field beam focusing of thesingle metallic subwavelength slit with the high permittivity of output space, wepropose a interference model of the quasi-cylindrical waves scattered by the metallicslit, with accompany of the secondary light sources radiation processes. According tothe theory, the quasi-cylindrical waves are firstly scattered from the slit exit corners,and then they have a spatial interference to form the periodic intensity fringes, whichcan be acted as the secondary light sources to thereafter reemit electromagnetic waveswith the phase coherence. And their subsequent spatial interference in the near-fieldregion finally leads to the beam focusing of the transmission light. The theoreticalpredictions agree well with the simulation results. We believe that this theoryprovides a new sight into the physical interaction of the subwavelength metallicstructures and incident light waves.
引文
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