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Surface plasmon polaritons (SPPs), which arise from the collective oscillations of the free electron gas in noble metals, are electromagnetic waves highly confined on the metal dielectric interface[1-2]. The promising properties of SPPs have led to various applications in modern science and technology, such as biological and chemical sensing[3-5], near field imaging[6-7], and enhanced optical transmission[8]etc. As the nature link between optics and electronics, SPPs are recently used to combine the two subjects to overcome the terahertz gap[9-13], which is still a great challenge for electromagnetic science. In these studies, metal or graphene SPPs are excited by parallel moving electron beam and transformed into coherent and tunable light radiation[9-10]or terahertz radiation[11-13], respectively. This opens a new way for radiation sources and SPPs applications.
The excitation of SPPs has been studied for a long time. The incident plane waves can be coupled into SPPs with lens, grating or sub-wavelength slits[1-2, 14-16]. Another SPPs excitation approach often used is the electrical dipoles, and the propagation direction of the excited SPPs can be controlled by the arrangement and polarizations of the dipoles[17-19]. Perpendicularly moving electron beam is also a powerful instrument to excite SPPs due to the development of scanning electron microscope[20-21]. Recently, the experimental and theoretic analysis show that SPPs can also be excited by parallel moving electron beam[22-26], and the excited SPPs have their unique properties: coherent, tunable, propagating along the electron beam without attenuation or additional radiation, such as transition radiation[23]. However, there are also many challenges in the parallel electron beam excitation. For example, the parallel electron beam should be very near to the metal surface. Even though the parallel excited SPPs propagate without attenuation, but they also decay with time for the energy loss in the metal.
In this paper, SPPs coupling excitation is presented to overcome these challenges in parallel electron beam excitation. For this excitation, a parallel moving electron beam is used to excite the mimicking surface plasmon polariotons (MSPPs)[27] on a nano-slits array, which are placed above the metal surface, and the excited MSPPs will be coupled into SPPs when they satisfy the boundary conditions. Based on this mechanism, SPPs can be coupled efficiently, regardless of the distance between the metal surface and the electron beam. The decay time of the coupled SPPs is as long as that of the excited MSPPs, and the amplitudes of the coupled SPPs are two orders of magnitude larger than that of SPPs excited by electron beam directly.
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The schematic of the SPPs coupling excitation is shown in Fig. 1a. A nano-slits array is placed above the semi-infinity metal. In the simulations of this letter, the parameter along X direction is selected to be much larger than that along Y and Z direction. To simplify the discussion, the nano-slits array is perfect electric conductor (PEC) and the metal is Ag, whose permittivity is described by the modified Drude model[9, 28]:
$${{\varepsilon }_{\text{Ag}}}(\omega )={{\varepsilon }_{\infty }}-{{{\omega }_{p}}^{2}}/{({{\omega }^{2}}-\text{i}\gamma \omega }\;)$$ (1) where ${\varepsilon _\infty } = 5.3, {\omega _p} = 1.39 \times {10^{16}}$rad/s, $\gamma = 3.21 \times {\kern 1pt} {10^{13}}{\kern 1pt} $ Hz[9, 28]. When an electron beam moves parallel to the nano-slits array, MSPPs will be excited on the surfaces of the array. The excited MSPPs, but not the evanescent waves produced by the electron beam directly, can be used to couple SPPs on the metal surface when they satisfy the boundary conditions of SPPs excitation.
The dispersion curves of SPPs coupling excitation are shown in Fig. 1b, in which D is 100 nm, a is 40 nm, h is 125 nm and hm is 200 nm. It can be seen that the dispersion curve of the MSPPs is close to that of the metal SPPs under the periodical boundary conditions. This indicates that the operating frequency and phase velocity of the excited MSPPs are the same as that of SPPs. Accordingly the excited MSPPs can be coupled into SPPs on the metal surface, as shown in the inset of Fig. 1b.
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摘要: 提出了一种电子注激励表面等离子体激元(SPPs)的新机制。平行运动电子注首先激励微纳缝阵列上的仿表面等离子体激元(MSPPs),以被激励的MSPPs为源耦合激励金属表面的相干可调的SPPs。数值计算与粒子模拟的结果表明该激励方式对于激励SPPs具有重大的优势。基于这种机制,SPPs能被距离金属表面任意远的电子注有效激励耦合。耦合激励的SPPs的衰减时间与被激励的MSPPs一致,其场幅值比同等条件下电子注直接激励的SPPs场幅值大两个数量级。因此,这种新的激励机制可能对SPPs的应用具有重大意义。Abstract: A novel mechanism of surface plasmon polaritons (SPPs) electron beam excitation is presented in this paper. The mimicking surface plasmon polaritons (MSPPs) on the nano-slits array excited by parallel moving electron beam are used to couple coherent and tunable SPPs on the metal surface. The results of numerical calculations and particle-in-cell simulations show that it brings many significant advantages to SPPs excitation. Based on this mechanism, SPPs can be coupled efficiently, regardless of the distance between the metal surface and the electron beam. The decay time of the coupled SPPs is as long as that of the excited MSPPs, and the amplitudes of the coupled SPPs are two orders of magnitude larger than that of SPPs excited by electron beam directly. Accordingly, this mechanism may bring great significances for the applications of SPPs.
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Key words:
- coupling excitation /
- electron beam /
- nano-slits array /
- surface plasmon polaritons
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