Compact and highly-confined spoof surface plasmon polaritons with fence-shaped grooves

In this paper, a compact and highly-confined spoof surface plasmon polaritons (SSPPs) with fence-shaped grooves is proposed. By adding the metal strips that similar to the fence on the basis of T-grooves, the waves can be confined more tightly as the propagation paths of current are effectively increased, which leads to a reduction of the height of SSPPs units by 48.4% compared to the rectangular grooves. Moreover, compared with conventional SSPPs units mentioned before, the proposed design exhibits the strongest confinement to EM waves. To verify the effectiveness of the proposed unit, a corresponding transmission line is simulated and fabricated. Both simulated and measured results are in good agreement, which show the superior performance of this structure. Meanwhile, due to the simplicity and effectiveness, this proposed structure has a great research and application prospects in developing the miniaturized devices and circuits.

structures, which are rectangular grooves, V-grooves, dumbbell grooves, trapezoidal grooves, T-grooves and parallel-arranged grooves. All the parameters can be adjusted according to the actual model to obtain the different degrees of limitations on EM waves.
In order to compare the limitation of EM waves of different structures shown in Fig. 1. The above parameters and w 3 appears in Fig. 1(h) are set as H = 9.5 mm, h = 4 mm, p = 1 mm, a = 4 mm, d = 5 mm, w 1 = 0.5 mm, w 2 = 0.5 mm, l 1 = 0.5 mm, l 2 = 0.75 mm, w 3 = 0.5 mm, in which the variables can be controlled effectively and make the results more convincing. The commercial simulation software CST is used to analyze the dispersion characteristics of these units. It can be clearly seen in Fig. 2(a) that the cut-off frequency of V-grooves is the biggest, which is 15.96 GHz, followed by rectangle grooves (12.15 GHz,11.88 GHz), dumbbell grooves(10.28 GHz), trapezoidal grooves(9.3 GHz), T-grooves(8.74 GHz), parallel-arranged grooves(7.82 GHz) and fence-shaped grooves(6.14 GHz), which is the smallest. It indicates that the proposed unit has the strongest confinement to EM waves. Simultaneously, to investigate the influence of different parameters on the dispersion relations of the proposed unit, the number of fence-shaped metal strips loaded on T-grooves, which is assigned as k equals to 2, 4 and 6. Moreover, the w 2 is given as 0.5 mm, 1.5 mm and 2.5 mm respectively to get their dispersion curves.
The simulated results of the above cases are shown in Fig. 2, from which it can be found that whether the number of metal strips is more or w 2 is smaller, the factor that changes with them is only the current path which is marked by letter l becomes longer and results show that the cut-off frequency decreases. Therefore, it can be concluded that the cut-off frequency is not only determined by the groove depth h, but also by the length of the current path l. Moreover, the fence-shaped grooves can reach a decrease of 48.4% in height compared with rectangular grooves which will benefit the miniaturization of circuits definitely.
The current distributions of the proposed grooves and rectangular grooves are simulated and shown in Fig. 3(a,b). It can be clearly seen that the propagation path of the current in fence-shaped grooves is much longer than that in rectangular grooves, which proves the previous inference.
Meanwhile, as shown in Fig. 3(c,d), the confinement of EM waves is much more significant in fence-shaped grooves than that in rectangular grooves.
The simulated and measured results of the proposed SSPPs waveguides with fence-shaped grooves. Based on the proposed structure, a transmission line shown in Fig. 4(a) is designed which completes the transition of rectangular grooves, T-grooves and finally, the fence-shaped grooves that displayed in part (I), (II) and (III), respectively. As the microstrip feeding structure is adopted here, this line is divided into three layers, the upper and lower layers are copper sheets with the thickness of 0.018 mm that are used to fabricate the transmission part and ground plane, and the middle layer is dielectric substrate made of Rogers 5880, whose thickness and dielectric constant are 0.508 mm and 2.2, respectively. Meanwhile, due to the three-layer structure   www.nature.com/scientificreports www.nature.com/scientificreports/ of this structure. Figure 5 shows the electric-field distributions in five different cross sections A, B, C, D, E that marked in Fig. 4, which not only clarifies that the electric field is restricted under the SSPPs units tightly, but also demonstrates the gradual transition of the field from microstrip line to SSPPs clearly.
Furthermore, to verify the functionality of the SSPPs with fence-shaped grooves, a device shown in Fig. 6(a) is made and tested according to the size and materials of the transmission line. The S-parameter of this line is measured by Vector Network Analyzer (N5247A) and the simulated and measured results are compared in Fig. 6(b). Due to the existence of machining error, testing errors and errors caused by human factors, all of these will lead to the difference between simulated and measured results. Despite these errors, it is clear from the Fig. 6(b) that the two results are in good agreement and |S 11 | is less −10 dB from 0.6 GHz to 5 GHz, while |S 21 | is higher than −1dB from 0.5 GHz to 4 GHz, which not only indicate the efficient transmission of this line, but also prove the validity of the proposed structure.

Conclusions
In summary, a novel spoof surface plasmon polaritons with fence-shaped grooves of compact size is proposed in this paper. For the propagation path of current is effectively increased, the fence-shaped grooves possess the strongest confinement to EM waves compared with other SSPPs units, which can be well utilized in the size reduction. For validation, a transmission line based on it is simulated and fabricated, the results of both are in good agreement and show the great performance of this structure. Due to the simplicity and maneuverability the