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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]:
Figure 1. The schematic and dispersion relation of SPPs coupling excitation
$${{\varepsilon }_{\text{Ag}}}(\omega )={{\varepsilon }_{\infty }}-{{{\omega }_{p}}^{2}}/{({{\omega }^{2}}-\text{i}\gamma \omega }\;)$$ (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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The electric fields in time domain of SPPs for coupling excitation and direct electron beam excitation (the distance between the electron beam and metal surface is 70 nm) are shown in Fig. 2a. It is illustrated in this figure that the SPPs coupled by MSPPs have a much longer decay time compared to that directly excited by electron beam. This is because that the excited MSPPs, which are the sources for the SPPs coupling excitation, can be kept in a very long time once they are excited by the electron beam. But for the direct electron beam excitation without MSPPs coupling, the evanescent waves produced by electron beam are the sources for the excitation, and they are only pulses with plenty of frequency components[23].
Figure 2. The coupled SPPs
Then there is a much longer interaction time between the SPPs and excitation source for the coupling excitation of SPPs than that of direct electron beam excitation. Therefore, the SPPs can get energy from the excited MSPPs continuously to compensate the energy loss due to the propagation loss of SPPs. Accordingly, the SPPs coupled by MSPPs have a very long decay time, which can be as long as that of the excited MSPPs.
As shown in Fig. 2b, the operating frequencies of the coupled SPPs are 841 THz and 810 THz for beam energy 80 keV and 200 keV, respectively. This is because that when the parallel moving electron beam excites the nano-slits array, the operating frequencies of the excited MSPPs are determined by the working points, which are the intersection points of the dispersion curve and the beam line, as shown in Fig. 1b. According to the boundary conditions of SPPs excitation, the operating frequency of the coupled SPPs is determined by that of the excited MSPPs. So the operating frequency of the coupled SPPs can also be tuned by adjusting the beam energy.
The frequency spectrum of the directly excited SPPs is also shown in Fig. 2b to make a comparison. It can be seen that the filed amplitude of the coupled SPPs is two orders of magnitude larger than that of SPPs directly excited by electron beam. This is because that the amplitude of the excited MSPPs is much larger than that of the evanescent waves produced by electron beam directly at the same operating frequency, and there is a much longer interaction time as mentioned above.
Further research shows that SPPs can also be coupled effectively by MSPPs on the nano-slits array with deeper slits depth. The dispersion curves at the structure parameters D=100 nm, a=30 nm, h=300 nm, hm=200 nm are shown in Fig. 3a. It can be seen that there are fundamental and high order modes for MSPPs, and the dispersion curve of the latter is close to that of SPPs. So, the excited high order mode MSPPs can be coupled into SPPs on the metal surface, but the fundamental mode cannot due to the mismatch of the boundary conditions of SPPs excitation, as shown in the contour maps in the insets of Fig. 3a. The observed frequency spectra in Fig. 3b show that the amplitude of the MSPPs coupled SPPs is two orders of magnitude larger than that of SPPs directly excited by electron beam at the same place. These results indicate that SPPs can be coupled by MSPPs excited by electron beam efficiently with suitable nano-slits array, regardless of the distance between the metal surface and the electron beam. This is because that the excited MSPPs propagate as plane waves in the slits (or guided modes in nano-holes) without energy loss[29].
Figure 3. The coupled SPPs by the nano-slits array with deeper slits depth
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In summary, a novel mechanism of SPPs electron beam excitation is presented in this letter. The physics of this mechanism is that the parallel moving electron beam first excites the MSSPs on the nano-slits array, which is placed above the metal surface with suitable parameters. And then the excited MSPPs, which are the real excitation source, can be coupled into coherent and tunable SPPs on the metal surface. This brings many significant advantages to the SPPs excitation. The SPPs coupled by MSPPs have a very long decay time, which can be as long as that of the excited MSPPs in principle. This makes the continuously output of SPPs possible. The amplitudes of the coupled SPPs are two orders of magnitude larger than that of directly excited SPPs. SPPs can be coupled by MSPPs efficiently with suitable nano-slits array, regardless of the distance between the metal surface and the electron beam. SPPs of other materials can also be generated by this mechanism, such as graphene SPPs, which cover the whole terahertz region with great applications. Accordingly, based on this mechanism, coherent and tunable SPPs can be coupled by MSPPs excited by electron beam, which has great significances for the applications of SPPs
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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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