亚衍射表面等离激元波导的光学性质
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摘要
表面等离激元学是基于表面等离激元(surface plasmon polaritons, SPP)的光子学。SPP是由金属一电介质界面支持的表面波。它是自由空间中的电磁波和金属表面附近电子等离子体振荡相耦合的结果。SPP的波矢大于电介质中相同频率光子的波矢。因此,利用SPP可以在亚波长尺度上实现对光的操纵。科研人员已经在理论上和实验上论证、分析了很多表面等离激元学器件。与受到衍射极限限制的经典光子学器件不同的是,表面等离激元学器件的尺度在可见光和近红外波段可以降低到微纳量级。
在表面等离激元学器件中,表面等离激元波导对SPP的传导和局域起到了重要作用。一般地,适合芯片集成的表面等离激元波导可以分为三种基本类型：绝缘体一金属(IM)型、绝缘体一金属—绝缘体(IMI)型以及金属—绝缘体—金属(MIM)型(这里绝缘体和金属分别用字母I和M表示)。本论文理论研究了这些基本类型表面等离激元波导的光学性质。尤其是,研究了绝缘层折射率为阶跃分布的MIM型波导的光学性质,以及MIM和IMI型波导中纵向电场为对称分布的SPP本征模式的激发问题。
研究发现,MIM型波导的功能可以通过在绝缘层中引入阶跃折射率调制而得到增强。此时,MIM波导变成了金属—多层绝缘体—金属(metal-multi-insulator-metal, MMIM)波导。我们系统地研究了两种包含三个绝缘层的对称的MMIM波导。给出了波导中SPP本征模式的有效折射率、能量局域化尺度、传播长度以及品质优值等光学性质随着波导几何参数的变化关系。由于受到阶跃调制折射率的影响,MMIM波导的这些光学性质不同于MIM波导。我们在MMIM波导中发现了三个厚度临界值。当相应绝缘层厚度等于厚度临界值时,本征模式的有效折射率的实部不随着其他绝缘层厚度的变化而变化。我们给出了厚度临界值所满足的关系式,并且根据MIM型波导的性质,对厚度临界值的存在做出了解释。另外,MMIM波导的光学性质取决于几何参数和芯层折射率分布。和MIM波导相比,MMIM波导可以实现更小的能量局域化尺度或者更大的传播长度。对于芯层厚度为几百个纳米的MMIM波导,可以实现高达103um的传播长度以及高达104的品质优值。
对称的MIM和IMI波导可以支持两种表面等离激元本征模式。根据模式纵向电场分量的对称性,将它们分别命名为反对称束缚模和对称束缚模。在MIM波导中,反对称束缚模的损耗相对较低,所以更适合于用来传导信号；而对称束缚模具有较高的能量密度,更适合于实现光和物质相互作用。在IMI波导中,通常情况下,反对称束缚模和对称束缚模的传播长度都足以实现在表面等离激元学纳米器件中操纵光的目的。然而,与对称束缚模相比,反对称束缚模具有更大的模式宽度,限制了IMI波导的集成密度。在MIM和IMI波导中,模式的横向电场分量的对称性决定了反对称束缚模可以通过很多途径激发出来,而对称束缚模则难以被激发出来。
为了便于在MIM波导中实现多功能光操纵以及提高IMI波导的集成密度,我们分别在MIM和IMI波导中设计了可以将反对称束缚模转换为对称束缚模的模式转换器。通过调整相位和功率密度分布,我们在两种对称性的SPP导模之间实现了高效率的模式转换。转换器是借助变换光学理论设计完成的,其中只包括由线性坐标变换得到的均匀的材料。我们在MIM波导中提出了两种实用的模式转换器结构。用有限元法模拟验证了转换器的功能。在不考虑传导损耗的情况下,实现了高达95%的模式转换效率。在考虑金属欧姆损耗的情况下,实现了超过80%的模式转换效率。同时,在IMI波导中,在考虑实际金属损耗的情况下,仅通过调整模式的相位分布,实现了～80%的模式转换效率。
Plasmonics is photonics based on surface plasmon polaritons (SPPs). SPPs, which are supported by metal-dielectric interfaces, are electromagnetic waves in the free space coupled to electron plasma oscillations in the metal surfaces. SPPs'wavevectors are greater than those of photons in the dielectrics with the same frequencies, enabling light manipulations in the sub-wavelength scales. A lot of plasmonic devices have been demonstrated and analyzed theoretically and experimentally. While conventional photonic devices suffer from the diffraction limit, their plasmonic counterparts can be downsized to micro-or nano-scales at visible and near infrared frequencies.
In plasmonic devices, plasmonic waveguides play an essential role for guiding and confining SPPs. In general, plasmonic waveguides that are suitable for on-chip integration can be modeled into three basic types:insulator-metal (IM), insulator-metal-insulator (IMI), and metal-insulator-metal (MIM). In this dissertation, the optical properties of the basic types of plasmonic waveguides are theoretically investigated. Particular attention is paid to MIM type plasmonic waveguides with step refractive index insulators, and the excitation of the plasmonic eigenmodes with symmetric longitude electric fields in both MIM and IMI waveguides.
The performances of MIM waveguides can be enhanced by introducing step refractive index modulation to the insulators, in which case the MIM waveguides change into metal-multi-insulator-metal (MMIM) waveguides. We systematically study two types of symmetric MMIM waveguides consisting of three insulators. The effective refractive index, energy confinement, propagation length, and figure-of-merit are given in terms of the geometric parameters. Due to the step refractive index modulation, these properties of MMIM waveguides differ from the MIM waveguides. Three critical thicknesses are found in MMIM waveguides. When the thickness of the associated insulator is equal to a critical thickness, the effective refractive index of the corresponding eigenmode keeps unchanged with the thickness of the other insulator. We give the expressions for the critical thicknesses and explain their existences by the properties of MIM type waveguides. Moreover, compared with the MIM waveguides, MMIM can possess either better energy confinement or larger propagation length, which depends on the geometric parameters and the refractive index distribution. Propagation length of up to103μm and figure-of-merit of up to104are observed for MMIM waveguide with core thickness of several hundred nanometers.
Symmetric MIM and IMI waveguides can support two types of plasmonic eigenmodes, namely the anti-symmetric bound (ab) mode and the symmetric bound (sb) mode according to the symmetry of the longitude electric field component. In MIM waveguides, the ab mode has relatively low loss, hence is better for signal transmission; while the sb mode has larger energy density and is better for light-matter interactions. In IMI waveguides, typically, both the ab and sb modes'propagation lengths are large enough for light manipulations in nano-plasmonic devices. However, compared with the sb mode, the mode width of the ab mode is much larger, limiting the integration density of IMI waveguides. Due to the symmetries of the lateral field components, in both MIM and IMI waveguides, the ab mode can be easily excited by many approaches, but the sb mode is difficult to launch.
In order to facilitate multifunctional manipulations of light in MIM waveguides and increase the integration density of IMI waveguides, we design mode converters in MIM and IMI waveguides that can convert the ab mode to the sb mode. Efficient conversion between the two types of modes can be achieved by reshaping both phase and power density distributions of the guided mode. The converters are designed with the assistance of transformation optics and only consist of homogeneous materials yielded from linear coordinate transformations. We propose two practical configurations of mode converter in MIM waveguides. The functionalities of the converters are demonstrated by finite element simulations. Without consideration of transmission loss, conversion efficiency of as high as95%can be realized. When ohm loss generated by the metallic regions is considered, the conversion efficiency is more than80%. In addition, conversion efficiency of-80%can be realized in IMI waveguides with real metals by only phase reshaping.
在表面等离激元学器件中,表面等离激元波导对SPP的传导和局域起到了重要作用。一般地,适合芯片集成的表面等离激元波导可以分为三种基本类型：绝缘体一金属(IM)型、绝缘体一金属—绝缘体(IMI)型以及金属—绝缘体—金属(MIM)型(这里绝缘体和金属分别用字母I和M表示)。本论文理论研究了这些基本类型表面等离激元波导的光学性质。尤其是,研究了绝缘层折射率为阶跃分布的MIM型波导的光学性质,以及MIM和IMI型波导中纵向电场为对称分布的SPP本征模式的激发问题。
研究发现,MIM型波导的功能可以通过在绝缘层中引入阶跃折射率调制而得到增强。此时,MIM波导变成了金属—多层绝缘体—金属(metal-multi-insulator-metal, MMIM)波导。我们系统地研究了两种包含三个绝缘层的对称的MMIM波导。给出了波导中SPP本征模式的有效折射率、能量局域化尺度、传播长度以及品质优值等光学性质随着波导几何参数的变化关系。由于受到阶跃调制折射率的影响,MMIM波导的这些光学性质不同于MIM波导。我们在MMIM波导中发现了三个厚度临界值。当相应绝缘层厚度等于厚度临界值时,本征模式的有效折射率的实部不随着其他绝缘层厚度的变化而变化。我们给出了厚度临界值所满足的关系式,并且根据MIM型波导的性质,对厚度临界值的存在做出了解释。另外,MMIM波导的光学性质取决于几何参数和芯层折射率分布。和MIM波导相比,MMIM波导可以实现更小的能量局域化尺度或者更大的传播长度。对于芯层厚度为几百个纳米的MMIM波导,可以实现高达103um的传播长度以及高达104的品质优值。
对称的MIM和IMI波导可以支持两种表面等离激元本征模式。根据模式纵向电场分量的对称性,将它们分别命名为反对称束缚模和对称束缚模。在MIM波导中,反对称束缚模的损耗相对较低,所以更适合于用来传导信号；而对称束缚模具有较高的能量密度,更适合于实现光和物质相互作用。在IMI波导中,通常情况下,反对称束缚模和对称束缚模的传播长度都足以实现在表面等离激元学纳米器件中操纵光的目的。然而,与对称束缚模相比,反对称束缚模具有更大的模式宽度,限制了IMI波导的集成密度。在MIM和IMI波导中,模式的横向电场分量的对称性决定了反对称束缚模可以通过很多途径激发出来,而对称束缚模则难以被激发出来。
为了便于在MIM波导中实现多功能光操纵以及提高IMI波导的集成密度,我们分别在MIM和IMI波导中设计了可以将反对称束缚模转换为对称束缚模的模式转换器。通过调整相位和功率密度分布,我们在两种对称性的SPP导模之间实现了高效率的模式转换。转换器是借助变换光学理论设计完成的,其中只包括由线性坐标变换得到的均匀的材料。我们在MIM波导中提出了两种实用的模式转换器结构。用有限元法模拟验证了转换器的功能。在不考虑传导损耗的情况下,实现了高达95%的模式转换效率。在考虑金属欧姆损耗的情况下,实现了超过80%的模式转换效率。同时,在IMI波导中,在考虑实际金属损耗的情况下,仅通过调整模式的相位分布,实现了～80%的模式转换效率。
Plasmonics is photonics based on surface plasmon polaritons (SPPs). SPPs, which are supported by metal-dielectric interfaces, are electromagnetic waves in the free space coupled to electron plasma oscillations in the metal surfaces. SPPs'wavevectors are greater than those of photons in the dielectrics with the same frequencies, enabling light manipulations in the sub-wavelength scales. A lot of plasmonic devices have been demonstrated and analyzed theoretically and experimentally. While conventional photonic devices suffer from the diffraction limit, their plasmonic counterparts can be downsized to micro-or nano-scales at visible and near infrared frequencies.
In plasmonic devices, plasmonic waveguides play an essential role for guiding and confining SPPs. In general, plasmonic waveguides that are suitable for on-chip integration can be modeled into three basic types:insulator-metal (IM), insulator-metal-insulator (IMI), and metal-insulator-metal (MIM). In this dissertation, the optical properties of the basic types of plasmonic waveguides are theoretically investigated. Particular attention is paid to MIM type plasmonic waveguides with step refractive index insulators, and the excitation of the plasmonic eigenmodes with symmetric longitude electric fields in both MIM and IMI waveguides.
The performances of MIM waveguides can be enhanced by introducing step refractive index modulation to the insulators, in which case the MIM waveguides change into metal-multi-insulator-metal (MMIM) waveguides. We systematically study two types of symmetric MMIM waveguides consisting of three insulators. The effective refractive index, energy confinement, propagation length, and figure-of-merit are given in terms of the geometric parameters. Due to the step refractive index modulation, these properties of MMIM waveguides differ from the MIM waveguides. Three critical thicknesses are found in MMIM waveguides. When the thickness of the associated insulator is equal to a critical thickness, the effective refractive index of the corresponding eigenmode keeps unchanged with the thickness of the other insulator. We give the expressions for the critical thicknesses and explain their existences by the properties of MIM type waveguides. Moreover, compared with the MIM waveguides, MMIM can possess either better energy confinement or larger propagation length, which depends on the geometric parameters and the refractive index distribution. Propagation length of up to103μm and figure-of-merit of up to104are observed for MMIM waveguide with core thickness of several hundred nanometers.
Symmetric MIM and IMI waveguides can support two types of plasmonic eigenmodes, namely the anti-symmetric bound (ab) mode and the symmetric bound (sb) mode according to the symmetry of the longitude electric field component. In MIM waveguides, the ab mode has relatively low loss, hence is better for signal transmission; while the sb mode has larger energy density and is better for light-matter interactions. In IMI waveguides, typically, both the ab and sb modes'propagation lengths are large enough for light manipulations in nano-plasmonic devices. However, compared with the sb mode, the mode width of the ab mode is much larger, limiting the integration density of IMI waveguides. Due to the symmetries of the lateral field components, in both MIM and IMI waveguides, the ab mode can be easily excited by many approaches, but the sb mode is difficult to launch.
In order to facilitate multifunctional manipulations of light in MIM waveguides and increase the integration density of IMI waveguides, we design mode converters in MIM and IMI waveguides that can convert the ab mode to the sb mode. Efficient conversion between the two types of modes can be achieved by reshaping both phase and power density distributions of the guided mode. The converters are designed with the assistance of transformation optics and only consist of homogeneous materials yielded from linear coordinate transformations. We propose two practical configurations of mode converter in MIM waveguides. The functionalities of the converters are demonstrated by finite element simulations. Without consideration of transmission loss, conversion efficiency of as high as95%can be realized. When ohm loss generated by the metallic regions is considered, the conversion efficiency is more than80%. In addition, conversion efficiency of-80%can be realized in IMI waveguides with real metals by only phase reshaping.
引文
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