二维金属纳米缝阵列的聚焦特性研究
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摘要
表面等离子体激元（Surface Plasmon Polariton, SPP）是由光和金属表面自由电子相互作用所激发的一种特殊电磁场。它被强烈地约束在金属表面，且能在亚波长尺度波导内传输，因而引起很多研究者的兴趣。利用SPP可以实现超衍射极限的集成光子学器件。由于现代光学器件对小型化和集成化的需求不断提高，基于SPP的亚波长光学器件得到大力发展。其中，金属纳米缝阵列由于在空间场调制和亚波长聚焦上独特的能力，引起了科研工作者的特别关注。本文基于SPP的基本理论，利用数值模拟方法研究了几种基于不同机制而设计的典型二维金属纳米缝透镜的聚焦性能。本论文主要的内容包括如下：
首先，研究了带有深度调制狭缝的小f数二维金属纳米缝透镜的聚焦性能。通过设计填充介质的金属狭缝来产生透镜所需的位相延迟，利用时域有限差分方法研究其聚焦性能，给出了焦点的大小、衍射效率、实际焦点位置以及归一化能量透过率。不同于传统电介质透镜，金属纳米缝透镜可以用作纯衍射元件，这是因为金属纳米缝透镜没有在弯曲表面发生光折射和全内反射以及由此所产生的能量损耗。对于传统电介质透镜， f数越小,则透镜的曲面曲率越大，光折射和全内反射越严重，因此产生的能量损耗越大。设计的小f数金属纳米缝透镜的衍射效率远远大于同样形状的电介质透镜的衍射效率。
第二，利用标量衍射理论分析了文献报道的柱状金属平板纳米缝透镜的焦移现象。给出了菲涅尔近似下的光轴能量分布公式并用于分析二维平板纳米缝透镜在远场区域的聚焦性能。结果表明相对焦移的大小只与菲涅尔数有关，透镜尺寸、预设焦距和入射波长对焦移的影响都源于菲涅尔数，透镜的总相位差近似等于菲涅尔数乘以π。利用时域有限差分方法获得的数值模拟结果和理论分析结果完全一致。此外，我们还利用光轴能量分布公式辅以简单的数值计算对之前的文献报道的焦移现象进行了分析，并计算了焦点的实际位置，计算结果与文献中的实验测量值符合的很好。
第三，提出了一种在缝内填充不同电介质的金属纳米缝阵列构成的二元表面等离子体激元透镜。通过调整缝内填充材料的折射率可以获得π大小的位相差。这种折射率调制的狭缝相比宽度调制狭缝在位相调制能力上具有明显的优势。这种二元结构既能保持了位相调制的优势又降低了制作难度。利用模拟退火算法，优化设计了几种具有不同功能的透镜结构，包括单焦点透镜、双焦点透镜以及具有角度补偿的透镜结构，并利用时域有限差分方法对其聚焦性能进行了验证。
第四，将渐变折射率散焦透镜嵌入到金属纳米缝阵列构造了具有会聚功能的金属透镜。当金属缝结构中缝缝间有耦合时，金属纳米阵列具有负折射现象。尽管渐变折射率金属透镜缝内介质的折射率分布和传统渐变折射率会聚透镜正好相反，但其色散曲线却和传统电介质渐变折射率会聚透镜相似。数值模拟结果证明，这种渐变折射率金属透镜能够将平面入射波会聚成一个深亚波长尺寸的焦点。我们研究了这种渐变折射率金属透镜的聚焦行为并且与传统的渐变折射率会聚透镜进行了比较。另外，我们还从理论分析和数值模拟两方面研究了这种透镜的外聚焦性质。
第五，通过交替堆叠金属和电介质弧形板构造了一种弯曲金属纳米缝阵列透镜。弯曲金属纳米缝阵列中的光线轨迹不是平行于缝而是向阵列内侧边界偏转。利用保角变换方法分析了弯曲金属纳米缝阵列的色散关系，其色散关系和单调渐变折射率透镜相似，从而证明了弯曲纳米缝阵列结构能够实现聚焦功能。对于一个平面入射波，我们利用数值方法验证了其能够在弯曲狭缝阵列中实现深度亚波长聚焦。数值模拟结果还表明其聚焦位置可以通过改变入射波长或者入射角来进行调节。
Surface plasmon polaritons are a special kind of electromagnetic field excited bythe interactions of light and free-electrons on the metal surface. It is greatly confined onthe metal surface and could propagate in subwavelength scale, and thus attracted manyresearch interest. The application of SPP enables the realization of integrated photonicdevices beyond the difraction limit. Much efort has been paid to develop SPP-basedsubwavelength devices in recent years because of the increasing demand for miniaturiza-tion and integration of modern optical device. Among them, the metallic nanoslit arrayhas received special attention due to its unique ability in spatial field modulation and sub-wavelength focusing. Based on the basic theory of SPP and using numerical simulationmethods, we investigated the focusing performance of several kinds of typical2D metallicslit lenses which are designed based on diferent mechanisms. The main content of thisthesis are summarized as follows:
First, the focusing performance of small f-number2D metallic lens with depth-modulated slits is studied. Metallic slits filled with dielectric are designed to producedesired optical phase retardation. Numerical simulation is performed through the finite-diference time-domain (FDTD) method. The focal spot size, the difraction efciency,the real focal position, and the normalized transmitted power are presented. Diferentfrom the conventional dielectric lens, the metallic lens can be used as a pure difractiveelement without energy loss brought by the light refraction at curved surfaces and totalinternal reflection. For the traditional dielectric lens, decreasing the f-number results insmaller radius of curvature. The energy loss brought by the light refraction and inner totalreflection will increase consequently. The difraction efciency of the designed metallicnanoslit lens with a small f-number is larger than that of dielectric lens with the sameshape.
Second, a theoretical analysis based on scalar2D difraction theory about the recent-ly reported focal-shift phenomena in planar metallic nanoslit lenses is given. An axial in-tensity formula is obtained under Fresnel approximation and used for the analysis of focalperformance in the far field zone of lens. It turns out that the relative focal shift is depen-dent with the Fresnel number only. The influences of the lens size, preset focal lengthand incident wavelength are all come from the change of Fresnel number. The total phase diference of the lens is almost equal to the Fresnel number multiplied by π. Numericalsimulations are performed using FDTD method and show agreement with the theoreticalanalysis. In addition, using the theoretical formula assisted by simple numerical method,we provide calculation results about the real focal position for the previous literatures.The results show great agreement with the experimental measurements provided by theliteratures.
Third, we propose a binary plasmonic lens based on metallic nanoslit array with d-iferent fillings. The phase range of π is achieved by changing the refractive indices ofthe filling materials in the slits. These index-modulated slits are demonstrated to have u-nique advantages in phase delay compared with the width-modulated ones. The proposedbinary structures can keep the advantage in phase modulation and reduce the difculty infabrication. Lenses with diferent functions, such as focusing light to one or two points orcorrecting oblique incident light, are designed using simulated annealing algorithm andchecked by finite-diference time-domain method.
Fourth, a gradient index (GRIN) diverging lens is embedded into a metallic slit arrayto form a gradient index metallic lens. Although the index distribution is opposite to thatof the traditional gradient index converging lens, the dispersive relations are similar. Wedemonstrate numerically that such gradient index metallic lens can converge a incidentplane wave into a deep-subwavelength focus. The focusing behavior is investigated andcompared with the traditional converging GRIN lens. In addition, the external focusing isalso investigated both numerically and analytically.
Fifth, a curved metallic slit array constructed by alternately stacking metal and di-electric arcs is considered. The light rays do not propagate parallel to the slits but deflectto inner boundary of the array. The conformal transformation is used to study the dis-persive relation of the curved metallic nanoslit array. The dispersive relation is similar tothat of a monotonically gradient index lens, which demonstrates the focusing ability ofthe curved nanoslit array. For a incident plane wave, we verified numerically that a focusof deep-subwavelength can be achieved in the inner slit. The numerical simulation resultsshow that the focusing position along the arc can be controlled by altering the incidentwavelength or the angle of incidence.
首先，研究了带有深度调制狭缝的小f数二维金属纳米缝透镜的聚焦性能。通过设计填充介质的金属狭缝来产生透镜所需的位相延迟，利用时域有限差分方法研究其聚焦性能，给出了焦点的大小、衍射效率、实际焦点位置以及归一化能量透过率。不同于传统电介质透镜，金属纳米缝透镜可以用作纯衍射元件，这是因为金属纳米缝透镜没有在弯曲表面发生光折射和全内反射以及由此所产生的能量损耗。对于传统电介质透镜， f数越小,则透镜的曲面曲率越大，光折射和全内反射越严重，因此产生的能量损耗越大。设计的小f数金属纳米缝透镜的衍射效率远远大于同样形状的电介质透镜的衍射效率。
第二，利用标量衍射理论分析了文献报道的柱状金属平板纳米缝透镜的焦移现象。给出了菲涅尔近似下的光轴能量分布公式并用于分析二维平板纳米缝透镜在远场区域的聚焦性能。结果表明相对焦移的大小只与菲涅尔数有关，透镜尺寸、预设焦距和入射波长对焦移的影响都源于菲涅尔数，透镜的总相位差近似等于菲涅尔数乘以π。利用时域有限差分方法获得的数值模拟结果和理论分析结果完全一致。此外，我们还利用光轴能量分布公式辅以简单的数值计算对之前的文献报道的焦移现象进行了分析，并计算了焦点的实际位置，计算结果与文献中的实验测量值符合的很好。
第三，提出了一种在缝内填充不同电介质的金属纳米缝阵列构成的二元表面等离子体激元透镜。通过调整缝内填充材料的折射率可以获得π大小的位相差。这种折射率调制的狭缝相比宽度调制狭缝在位相调制能力上具有明显的优势。这种二元结构既能保持了位相调制的优势又降低了制作难度。利用模拟退火算法，优化设计了几种具有不同功能的透镜结构，包括单焦点透镜、双焦点透镜以及具有角度补偿的透镜结构，并利用时域有限差分方法对其聚焦性能进行了验证。
第四，将渐变折射率散焦透镜嵌入到金属纳米缝阵列构造了具有会聚功能的金属透镜。当金属缝结构中缝缝间有耦合时，金属纳米阵列具有负折射现象。尽管渐变折射率金属透镜缝内介质的折射率分布和传统渐变折射率会聚透镜正好相反，但其色散曲线却和传统电介质渐变折射率会聚透镜相似。数值模拟结果证明，这种渐变折射率金属透镜能够将平面入射波会聚成一个深亚波长尺寸的焦点。我们研究了这种渐变折射率金属透镜的聚焦行为并且与传统的渐变折射率会聚透镜进行了比较。另外，我们还从理论分析和数值模拟两方面研究了这种透镜的外聚焦性质。
第五，通过交替堆叠金属和电介质弧形板构造了一种弯曲金属纳米缝阵列透镜。弯曲金属纳米缝阵列中的光线轨迹不是平行于缝而是向阵列内侧边界偏转。利用保角变换方法分析了弯曲金属纳米缝阵列的色散关系，其色散关系和单调渐变折射率透镜相似，从而证明了弯曲纳米缝阵列结构能够实现聚焦功能。对于一个平面入射波，我们利用数值方法验证了其能够在弯曲狭缝阵列中实现深度亚波长聚焦。数值模拟结果还表明其聚焦位置可以通过改变入射波长或者入射角来进行调节。
Surface plasmon polaritons are a special kind of electromagnetic field excited bythe interactions of light and free-electrons on the metal surface. It is greatly confined onthe metal surface and could propagate in subwavelength scale, and thus attracted manyresearch interest. The application of SPP enables the realization of integrated photonicdevices beyond the difraction limit. Much efort has been paid to develop SPP-basedsubwavelength devices in recent years because of the increasing demand for miniaturiza-tion and integration of modern optical device. Among them, the metallic nanoslit arrayhas received special attention due to its unique ability in spatial field modulation and sub-wavelength focusing. Based on the basic theory of SPP and using numerical simulationmethods, we investigated the focusing performance of several kinds of typical2D metallicslit lenses which are designed based on diferent mechanisms. The main content of thisthesis are summarized as follows:
First, the focusing performance of small f-number2D metallic lens with depth-modulated slits is studied. Metallic slits filled with dielectric are designed to producedesired optical phase retardation. Numerical simulation is performed through the finite-diference time-domain (FDTD) method. The focal spot size, the difraction efciency,the real focal position, and the normalized transmitted power are presented. Diferentfrom the conventional dielectric lens, the metallic lens can be used as a pure difractiveelement without energy loss brought by the light refraction at curved surfaces and totalinternal reflection. For the traditional dielectric lens, decreasing the f-number results insmaller radius of curvature. The energy loss brought by the light refraction and inner totalreflection will increase consequently. The difraction efciency of the designed metallicnanoslit lens with a small f-number is larger than that of dielectric lens with the sameshape.
Second, a theoretical analysis based on scalar2D difraction theory about the recent-ly reported focal-shift phenomena in planar metallic nanoslit lenses is given. An axial in-tensity formula is obtained under Fresnel approximation and used for the analysis of focalperformance in the far field zone of lens. It turns out that the relative focal shift is depen-dent with the Fresnel number only. The influences of the lens size, preset focal lengthand incident wavelength are all come from the change of Fresnel number. The total phase diference of the lens is almost equal to the Fresnel number multiplied by π. Numericalsimulations are performed using FDTD method and show agreement with the theoreticalanalysis. In addition, using the theoretical formula assisted by simple numerical method,we provide calculation results about the real focal position for the previous literatures.The results show great agreement with the experimental measurements provided by theliteratures.
Third, we propose a binary plasmonic lens based on metallic nanoslit array with d-iferent fillings. The phase range of π is achieved by changing the refractive indices ofthe filling materials in the slits. These index-modulated slits are demonstrated to have u-nique advantages in phase delay compared with the width-modulated ones. The proposedbinary structures can keep the advantage in phase modulation and reduce the difculty infabrication. Lenses with diferent functions, such as focusing light to one or two points orcorrecting oblique incident light, are designed using simulated annealing algorithm andchecked by finite-diference time-domain method.
Fourth, a gradient index (GRIN) diverging lens is embedded into a metallic slit arrayto form a gradient index metallic lens. Although the index distribution is opposite to thatof the traditional gradient index converging lens, the dispersive relations are similar. Wedemonstrate numerically that such gradient index metallic lens can converge a incidentplane wave into a deep-subwavelength focus. The focusing behavior is investigated andcompared with the traditional converging GRIN lens. In addition, the external focusing isalso investigated both numerically and analytically.
Fifth, a curved metallic slit array constructed by alternately stacking metal and di-electric arcs is considered. The light rays do not propagate parallel to the slits but deflectto inner boundary of the array. The conformal transformation is used to study the dis-persive relation of the curved metallic nanoslit array. The dispersive relation is similar tothat of a monotonically gradient index lens, which demonstrates the focusing ability ofthe curved nanoslit array. For a incident plane wave, we verified numerically that a focusof deep-subwavelength can be achieved in the inner slit. The numerical simulation resultsshow that the focusing position along the arc can be controlled by altering the incidentwavelength or the angle of incidence.
引文
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