The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons(SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach.We consider both asymmetric and symmetric structures.Especially,in the symmetric system,two possible modes can exist:the odd mode and the even mode.The dispersion relations of the two modes are obtained.Due to the nonlinear dielectric,the magnitude of the electric field at the interface appears and alters the dispersion relations.The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.     

Nonlinear s-polarized surface plasmon polaritons

We have examined the dispersion relations for s-polarized surface plasmon polaritons, guided by (a) the interface between a semi-infinite metal and dielectric medium, and (b) a metal film bounded by semi-infinite dielectric media for situations in which one or more of the dielectric media are characterized by an intensity-dependent refractive index. We found that s-polarized waves satisfy the dispersion relations for very thin metal films bounded by nonlinear dielectric media. These waves exist only for power levels above a threshold that depends on the material parameters. We also comment on the experimental feasibility of observing these waves.     

The complex dispersion relation of surface plasmon polaritons at gold/para-hexaphenylene interfaces

Two-photon photoemission electron microscopy (2P-PEEM) is used to measure the real and imaginary part of the dispersion relation of surface plasmon polaritons at different interface systems. A comparison of calculated and measured dispersion data for a gold/vacuum interface demonstrates the capability of the presented experimental approach. A systematic 2P-PEEM study on the dispersion relation of dielectric-loaded gold surfaces shows how effective the propagation of surface plasmon polaritons at a gold/para-hexaphenylene interface can be tuned by adjustment of the dielectric film thickness. Deviations of the experimental results from effective index calculations indicate the relevance of thin film peculiarities arising from the details of the growth process and corroborate the need of experimental analysis techniques for dispersion relation measurements.     

基于平面波导激励的修正长程表面波的传感器研究

为了解决传统的强度检测型波导激励的表面等离子体共振传感器灵敏度不高的缺点,研究平面波导激励的介质膜-金属-被测介质的可激发修正的长程表面等离子体波结构。采用离子交换的方法制备折射率可用费米函数拟合的平面波导,研究了离子交换时间对平面波导的模数及等效折射率等特性的影响,为激励波导的优化设计提供有效依据。采用制备的平面波导激励介质膜-金属-被测介质的非对称结构,研究金属材质、介质膜厚和金属膜厚等因素对修正的长程表面等离子体波特性的影响,对被测溶液的折射率进行检测。实验结果表明,其灵敏度为传统的强度检测型表面等离子体共振传感器的6倍,并且具有较好的线性关系。     

Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity

We demonstrate controlled squeezing of visible light waves into nanometer-sized optical cavities. The light is perpendicularly confined in a few-nanometer-thick SiO2 film sandwiched between Au claddings in the form of surface plasmon polaritons and exhibits Fabry-Perot resonances in a longitudinal direction. As the thickness of the dielectric core is reduced, the plasmon wavelength becomes shorter; then a smaller cavity is realized. A dispersion relation down to a surface plasmon wavelength of 51 nm for a red light, which is less than 8% of the free-space wavelength, was experimentally observed. Any obvious breakdowns of the macroscopic electromagnetics based on continuous dielectric media were not disclosed for 3-nm-thick cores.     

Analysis of surface and guided wave plasmon polariton modes in insulator–metal–insulator planar plasmonic waveguides

Theoretical and experimental study of the surface plasmon–polariton and guided wave plasmon polariton modes is presented for the Sapphire/Ag/Polycarbonate/Air structure. Theoretical results are obtained by solving complex multilayer eigenvalue equations as well as the reflectivity equation for this structure. It is proposed that the mode attenuation can be significantly reduced by inserting a low index dielectric buffer between the metal and the guiding dielectric layer. The dispersion and attenuation curves are generated. Both the surface plasmon and guided wave plasmon polariton modes are studied experimentally. The experimental values of the effective refractive indices agree well with the theoretical values. The electric field profiles are generated and used to examine the nature of modes. After optimization of various parameters the condition for low loss single mode guiding is obtained for the proposed structure. Effect of metal thickness on surface plasmon mode is also discussed. It is inferred that in a properly optimized plasmonic waveguide, the losses can be reduced by a factor of 4.     

SPM of nonlinear surface plasmon waveguides

Pulse propagation equation of nonlinear dispersion surface plasmon waveguide is educed strictly from wave equation. The nonlinear coefficient is defined and then used to assess and compare the nonlinear characteristic of three popular 1-D surface plasmon waveguides: the single metal–dielectric interface, the metal slab bounded by dielectric and the dielectric slab bounded by metal. SPM (self-phase modulation) of the typical surface plasmon waveguide is predicted and discussed.     

Enhanced optical transmission through a nanoslit by coupling light between periodic strips and metal film

Surface plasmon resonance （SPR） is obtained by exciting the surface plasmon （SP） at the metal and dielectric interface, which can greatly enhance the extraordinary optical transmission （EOT） through a nanoslit milled in the metal film. We present a structure with a 50-nm-wide silver nanoslit for EOT by coupling light into the dielectric interlayer between periodic strips and a metal film. When the period of the metallic strips is equal to the wavelength of the SPR, the transmission efficiency of 187.6 through the nanoslit is enhanced. The metallic strip width over the nanoslit is optimized to improve transmission efficiency, and the maximal efficiency of 204.3 is achieved.     

The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

Tunable Omnidirectional Surface Plasmon Resonance in Cylindrical Plasmonic Structure

The tunable omnidirectional surface plasmon resonance in the optical range is theoretically demonstrated in a cylindrical plasmonic crystal by using rigorous coupled-wave analysis. The cylindrical plasmonic crystal consists of an infinite chain of two-dimensional cylindrical metal--dielectric-dielectric-metal structures. The dispersion relation of the cylindrical plasmonic crystal is obtained by calculating the absorptance as a function of a TM-polarized incident plane wave and its in-plane wave vector. The omnidirectional surface plasmon resonance can be tuned from UV region to visible region by adjusting the thickness of the cylindrical dielectric layers. The absorption spectrum of the infinite chain of nanocylinders is also investigated for comparison.     

介质保护膜在表面等离子体波探测器中的应用研究

基于表面等离子体波共振技术的探测器中金属膜通常与被探测物直接接触,在金属膜和被探测物之间增加一层介质膜,可以对金属膜进行保护.为了优化探测器的设计,通过对四层共振结构中表面等离子体波共振吸收峰随保护层厚度及其介电常数变化的计算,得到了对保护层参量的选择条件.     

The determination of the thickness and the optical dispersion property of gold film using spectroscopy of a surface plasmon in the frequency domain

We propose to use wavelength modulation approach,i.e.,the spectroscopy of a surface plasmon in the frequency domain,to characterize the optical dispersion property of gold film.Using this method,we determine the dispersion relationship of gold film in a wavelength range from 537.12 nm to 905.52 nm,and our results accord well with the reported results by other authors.This method is particularly suited for studying the optical dispersion properties of thin metal films,because a series of dielectric constants over a wide spectral range can be determined simultaneously via only a single scan of the incident angle,thereby avoiding the repeated measurements required when using the angular modulation approach.     

Determination of thickness and optical dispersion property of gold film using spectroscopy of surface plasmon in frequency domain

We propose to use wavelength modulation approach, i.e., the spectroscopy of surface plasmon in frequency domain to characterize the optical dispersion property of gold film. Using this method, we determine the dispersion relationship of gold film in a wavelength range from 537.12 nm to 905.52 nm, and our results accord well with the reported results by other authors. This method is particularly suited for studying the optical dispersion properties of thin metal films, because a series of dielectric constants over a wide spectral range can be determined simultaneously via only a single scan of the incident angle, thereby avoiding the repeated measurements required when using angular modulation approach.     

Nonlinear dispersion relation for surface plasmon at a metal-Kerr medium interface

The dispersion relation for the plasmon at the interface of a metal and a nonlinear Kerr medium is studied by applying a semi-analytic theory established in the literature. Explicit analytical results are obtained and are compared to those from a certain approximate treatment appeared in the literature. It is found that for large electric field strengths, both the dispersion relation and the surface plasmon frequency from the approximate treatment deviate significantly from those obtained in the exact approach, especially for the case with a negative Kerr susceptibility.     

Slowing light in diatomic nanoshelled chains

Coupled plasmon modes have been studied theoretically in periodic chains of shelled and unshelled metal nanoparticles embedded alternatively in a dielectric host, thus forming a diatomic chain. We calculate the dispersion relation of the diatomic chains and show that we can tune the shelled particle band into the unshelled particle band by varying the permittivity contrast and/or the core-shell radius ratio. This offers a precise control of the group velocity of coupled plasmon modes. The experimental realization of such diatomic chains by surface plasmon enhanced binding will be discussed.     

Interaction between localized and propagating surface plasmons: Ag fine particles on Al surface

Samples consisting of Ag fine particles 4nm in size placed near to an Al surface were prepared by depositing Ag-SiO₂ composite films by a rf cosputtering method onto vacuum-evaporated Al films. Angle-scan attenuated total reflection (ATR) measurements were performed over a wide wavelength range (λ=350-630nm) covering the resonance region (λ-410nm) of localized surface plasmon (LSP) in the Ag particles. It was found that the existence of Ag fine particles near to the Al surface led to a deformation of the dispersion curve of the surface plasmon polariton (SPP) propagating on the Al surface, in particular, in the LSP resonance region. The interaction between LSP and SPP was found to become much stronger as the distance between the particles and the surface decreases. The theoretical calculations based on the effective medium theory, which gave an effective dielectric function of the Ag-SiO₂ composite film, reproduced the deformation of the dispersion curve of the SPP. The deformation of the dispersion observed experimentally was qualitatively explained by the behavior of the effective dielectric function of the Ag-SiO₂ composite film.     

表面等离子体共振控制镜面反射率

对金属介电常数随温度变化的计算进行了修正,提出了利用表面等离子体共振(SPR)实现温度控制镜面反射率的方法。在Kretschmann结构中的金属膜上涂覆热光系数较大的聚合物材料,考虑该结构中各种材料介电常数以及金属膜厚度随温度的变化,利用特征矩阵法进行了数值模拟,得到SPR反射率曲线随温度的变化。模拟结果显示,当波长为532nm的p偏振光分别以70°和75°入射时,在10℃～90℃范围内调节温度,可实现反射率在52.8%～41.5%和31.1%～18.8%范围内的调节。     

Dispersion of cylindrical surface plasmon polaritons in layered structures

The problem of the existence of cylindrical surface plasmon polaritons on thin metal conductors is considered. A dispersion relation is obtained and analyzed, the domain of existence of dispersion curve with a maximum is found, and parametric relations are derived.     

Surface plasmon dispersion relation for spherical metal particles

Using the hydrodynamical model, we have obtained the surface plasmon dispersion relation for spherical metallic particles in the following two cases: (1) a sharp surface cut off in electron density and (2) a diffused electron density at the surface. The diffused density is modelled with a step function. The diffuse nature of the electron density at surface of the metal particle is necessary to understand the experimental result for particles with small radii. Shift in the absorption frequency is estimated and found to be small.     

Magnetically tunable surface plasmon resonance based on a composite consisting of noble metal nanoparticles and a ferromagnetic thin film

We demonstrate magnetically tunable surface plasmon resonance based on a composite consisting of noble metal nanoparticles and ferromagnetic thin film. We found that both the frequency and linewidth of the localized surface plasmon resonance can be manipulated by applying an external magnetic field. The underlying mechanism is attributed to the variation of the dielectric constant in the ferromagnetic thin film resulting from the change of magnetization. Our result shown here paves an alternative route for manipulation of the characteristics of the surface plasmon resonance, which may serve as a new design concept for the development of magneto-optical devices.