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Abstract
Terahertz (THz) broadband spoof surface plasmon polaritons (SSPPs) using new structure of ultra-compact split-ring grooves are proposed. The high-order mode propagation is highly concentrated around the proposed structure with lower radiation loss implying improved operating bandwidth. More importantly, a size reduction of 83.5% can be realized as compared to the traditional grounded SSPP structure with the same high-order asymptotic frequency. To further verify the proposed idea, a similar structure in microwave regime is designed and measured, where the excitation is easily achieved by directly connecting the microstrip line to the proposed SSPP waveguide. The gradient transition section, such as flaring ground, can be avoided, which decreases the waveguide’s longitudinal and transversal lengths and simplifies the design procedure. The measured results of the microwave prototype illustrate that it has good lowpass filtering performance, in which the reflection coefficient is better than −10 dB up to 13 GHz, with the smallest and worst insertion losses of 0.5 dB and 4.5 dB, respectively. To the best of the authors’ knowledge, this work presents THz high-order broadband SSPP propagation for the first time, having significant potential for plasmonic integrated circuits application at microwave/THz frequencies.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves propagating along the metal-dielectric interface, which have attracted increasing attentions due to their remarkable capability of guiding and localizing EM waves into subwavelength scales during these two decades [1–3]. To expand the advantages and applications of SPPs from optical regime to lower frequencies, i.e., terahertz (THz) and microwave frequencies, spoof SPPs (SSPPs) were proposed by structured metal surfaces [4,5]. In [6], the development of SSPPs in recent years has been comprehensively reviewed focusing on the basic concept, theory, design method, and applications in microwave engineering. Moreover, the corresponding high-efficiency excitations for SSPP wave were also investigated, including flaring ground [7], tapered CPWs and gradient slots [8,9], etc. Base on the SSPP waveguides, many high-frequency devices have been presented, such as ultra-wideband filters [10–13], electronically switchable and tunable bandpass filters [14], band-stop filter [15], continuous leaky-wave scanning antennas [16], 4-way wavelength demultiplexer [17], frequency splitter [18,19], programmable SSPP logic “AND” gate [20], and lactose sensing with enhanced field confinement [21].
However, most of these SSPP structures have to occupy large areas for the excitation or mode-conversion designs, which pose challenges for size reduction of the SSPP-based integrated circuits. In addition, the existing SSPP structures mainly support the fundamental mode, only few reported on the characteristics of the high-order mode. This is because even though the high-order mode is excited, it is usually difficult to achieve broadband propagation along the waveguided structures due to the intrinsic weak field confinements caused by the dispersion characteristics [22]. More importantly, few researches on THz high-order SSPP propagation have been reported so far. Therefore, it is highly necessary to explore and realize THz broadband propagation of the high-order mode SSPPs with simple geometry and compact size.
In this paper, to tackle the aforementioned challenges, based on the grounded slotline with split-ring grooves, the THz high-order mode propagation of SSPPs with greatly improved bandwidth and corresponding SSPP waveguides with state-of-the-art size reduction are proposed. Compared with the traditional THz grounded-slotline SSPP structure, a size reduction of 83.5% has be achieved. The results from the dispersion analysis indicate a broadband high-order mode with strong field confinements. To verify the proposed idea, THz prototypes with different lengths are designed and simulated. Then, such prototypes are scaled down to microwave regime, fabricated and tested. The excitation of the high-order mode of SSPPs in microwave frequencies is accomplished by directly connecting microstrip lines to the proposed waveguides, which greatly decreases the proposed waveguide size by avoiding the flaring ground and gradient grooves. Both of the measurements and simulations validate high-efficiency THz broadband propagation of the high-order mode of SSPPs. This design provides a novel ultra-compact solution for THz high-order mode propagation of SSPPs, and may have promising potential application in biochemical sensors, high-resolution imaging, and novel microwave circuits.
2. Analysis of proposed THz high-order SSPP unit cell
Figure 1(a) illustrates the schematic view of the traditional THz slotline-based SSPP unit cell (Structure A) with two-side transversal grooves. For all the figures in this section, the orange and yellow colors indicate top and bottom thin metal films, respectively. The thickness of each metal film is 1 µm, and the sandwiched dielectric substrate by the two metal films has the thickness of 10 µm, relative permittivity of 3.5, and loss tangent of 0.003. The parameters W1 and L2 represent width and depth of the groove, while D and W0 denote the period and width of the longitudinal slot, respectively. Herein, a modified SSPP unit cell built by grounded slotline with two-side transversal grooves (Structure B) is proposed, and its structure is shown in Fig. 1(b). The main difference from the Structure A is that the back of the dielectric substrate is fully covered by a thin metal film, which is regarded as the ground plane. The two-side transversal grooves are the same as those shown in Fig. 1(a), while the width of the whole Structure B is reduced to W3. To further reduce the dimension, the geometry of the new unit cell (Structure C) is proposed as shown in Fig. 1(c), where the two-side grooves in Fig. 1(b) are replaced by two-side split-ring grooves. The width of the whole structure can be sharply condensed to W4, resulting in 83.5% reduction of transversal size compared with that of Structure B. The performance is also better than the recent reported microwave-band T-shaped plasmonic structure [22]. All the detailed geometrical parameters of the cells can be found in the caption of Fig. 1.
Fig. 1 Schematic configuration of the proposed THz SSPP unit cell. (a) Slotline with two-side transversal grooves (Structure A). (b) Grounded slotline with two-side transversal grooves (Structure B). (c) Grounded slotline with two-side split-ring grooves (Structure C). The detailed dimensions are D = 20 µm, L2 = 36.2 µm, L3 = 43 µm, W0 = 1.5 µm, W1 = 1 µm, W2 = 220 µm, W3 = 75.9 µm, W4 = 12.5 µm, W5 = 1 µm, and W6 = 1 µm. (d) Dispersion curves of the fundamental and high-order modes of different SSPP unit cells. The inset is the z-component electric field distributions of the first two modes of the Structure C unit cell.
To obtain the dispersion curves, theoretical calculations and numerical eigen-mode simulations are carried out by the commercial software, CST Microwave Studio. The dispersion characteristics of these three structures are investigated by placing the unit cells in an air box where the boundaries in the x direction should be set as the periodic boundaries, and the other boundaries in the y and z directions are set as the PEC boundaries. All eigen-frequencies are calculated when sweeping the phase difference between the two periodic boundaries from 0° to 180°. Hence, the dispersion relation of the fundamental and high-order modes are obtained as displayed in Fig. 1(d), where k denotes propagation constant in the x axis and the inset figure shows the z-component electric field distributions of the first two modes of the Structure C. The fundamental modes of these three structures all deviate significantly from the lightline, and those of the Structures A and B have the overlapped dispersion relations showing that the dispersion properties of the fundamental mode are not affected by the ground plane. However, the high-order mode of the Structure B presents much larger deviation compared with that of the Structure A, which means that the ground plane can be used to improve the field confinement of the high-order mode at low frequencies and broaden its operating bandwidth, since the dispersion curve of the Structure A is very close to the lightline implying very weak field confinements and relatively narrow operating band. Besides, it can be also seen that although the Structure C is much smaller than Structure B, the high-order asymptotic frequencies of these two structures are identical (i.e., approximately 1.45 THz). This means the area of the SSPP circuits to realize the broadband high-order mode propagation can be highly reduced by adopting the proposed topology (i.e., Structure C). To distinguish the propagating mode supported in the SSPP waveguide and thus to obtain clearer observation, the z-component electric field distributions of the first two modes of Structure C are illustrated in the inset of Fig. 1(d). The Mode 1 shows anti-symmetric distribution (i.e., fundamental odd mode), while Mode 2 exhibits symmetric property.
3. THz high-order SSPP waveguide developed from split-ring unit cells
Based on the split-ring grooves in Fig. 1(c), an ultra-compact THz SSPP waveguide is proposed with the number of the periodic unit cells denoted as N = 21, as shown in Fig. 2(a). The properties of the proposed SSPP waveguide are investigated by the frequency domain simulation, where the parameters of the dielectric substrate and the split-ring parts are the same as those of the above section. The THz signal is directly fed to the proposed structure by assigning excitation of waveguide port, and the open boundaries are applied in all directions to mimic the real space. Figure 2(b) displays the simulated intensities of the z-component electric fields at 1 and 1.3 THz, which are in the passband and stopband, respectively. Obviously, the electric fields at 1.3 THz suffer from sharp decrease when traveling through the feeding point, while the electric fields at 1 THz show much higher intensity. In addition, the electric field distributions on the x-y plane when z = 2 µm are demonstrated in the inset of Fig. 2(b). For fair comparison, both of these two electric field distributions have the same color bar in dB scaling. It is clearly observed that the SSPP propagation at 1.3 THz is highly attenuated, while for the SSPP propagation at 1 THz, almost no changes happen along the proposed structure. All the phenomena above prove that SSPP modes will be efficiently blocked beyond the cutoff frequency of the proposed plasmonic structure. Note that not only the surface EM waves at 1 THz but also the other signals whose operation frequencies are lower than cutoff frequency can efficiently propagate along the proposed THz SSPP waveguide.
Fig. 2 (a) Schematic configuration of the proposed THz SSPP waveguide. (b) Electric field intensities along x direction when y = 0 um and z = 2 µm. The dimensions of the proposed unit cells in the waveguide is the same as that in Fig. 1(c), and the number of the periodic unit cells N is set as 21. The inset of Fig. 2(b) shows the electric field distributions of 1 THz and 1.3 THz on the x-y plane when z = 2 µm.
To further obtain a clear insight into the SSPP propagation features of the proposed THz waveguide, the characteristics of both transmission and reflection are also simulated as seen in Fig. 3, where the ultra-wideband lowpass filtering performance can be achieved. Figure 3(a) illustrates that the bandwidth can be broadened as L3 decreases from 44 to 42 µm, which means that the bandwidth of the lowpass response can be adjusted by tuning the length L3 of the meandering groove. Additionally, the cases with different period numbers of unit cells have almost the same frequency response as seen in Fig. 3(b), which implies the unit cell numbers of the proposed SSPP waveguide are insensitive to the SSPP wave propagation.
Fig. 3 Simulated S-parameters of the proposed THz SSPP waveguide (a) with different groove lengths (L3 = 42, 43, 44 μm) and (b) with different periods (N = 21, 23, 25).
4. Design of microwave ultra-compact SSPP waveguide
Not only applied in THz band, the proposed SSPP waveguide also can be extended to microwave regime. As shown in Fig. 4, the microwave prototype is developed from the THz one with dimensions scaled up, and the input and output ports of microstrip lines are designed for excitation and mode conversions. The SSPP wave is converted from guided wave by directly connecting the microstrip lines with width of W7 to the proposed periodic array. The width of the microstrip section is carefully optimized to accomplish the impedance matching based on the subsequent analysis of the normalized impedance features of the proposed waveguide. Due to avoiding the gradient transition structure (e.g., flaring ground), the longitudinal and transversal lengths of the whole circuits can be potentially shortened, and the design process is greatly simplified.
Fig. 4 Schematic configuration of the proposed microwave SSPP waveguide with the input and output microstrip excitations and mode conversions. The detailed dimensions are D = 2.8 mm, L2 = 4 mm, L3 = 11.5 mm, W0 = 0.2 mm, W1 = 0.1 mm, W2 = 25.9 mm, W3 = 15 mm, W4 = 1.3 mm, W5 = 0.1 mm, and W6 = 0.2 mm. The number of the periodic unit cells N is set as 7.
To obtain clear insight into the mode conversion principle of this conversion-free waveguide structure, the dispersion relations and normalized impedances of the split-ring groove unit cell with different dimensions of W6 are depicted in Fig. 5. It can be observed in Fig. 5(a) that as the width W6 decreases from 0.25 to 0.15 mm with the step of 0.05 mm, the asymptotic frequency will be lower, indicating good momentum matching. We also extract the impedance of the proposed SSPP unit cell normalized to 50 Ω as shown in Fig. 5(b), where the normalized impedance is already very close to one, indicating excellent impedance matching between SSPP waveguide and 50-Ω microstrip line, even if no gradient transition section is applied. Moreover, the impedance of the SSPP waveguide will slightly increase approaching 50 Ω as W6 decreases, which means that such impedance can be tailored by changing the physical dimensions, while the characteristic impedance of the microstrip line can be also tuned by adjusting the width W7. Therefore, based on this impedance characteristics analysis, the matching work and corresponding mode conversion design can be carried out with the help of full-wave electromagnetic simulation. Finally, W7 = 1.35 mm and W6 = 0.15 mm are selected in this work. Without gradient transition structure, the proposed SSPP waveguides will show potentially smaller longitudinal and transversal dimensions, as compared to other circuits where the traditional mode conversion structures have to be employed.
Fig. 5 Mode conversion principle between guided wave and SSPPs wave. (a) Dispersion characteristics of the second mode and (b) normalized impedances of the proposed unit cell with different parameters of W6.
Figures 6(a) and 6(b) show the photographs of the fabricated SSPP waveguide with N = 7. In order to explore the excitation and propagation of the high-order mode of SSPPs, the z-component electric field distributions are simulated as shown in Figs. 6(c) and 6(d). It can be observed that the field patterns are symmetric, which indicates that the propagating waves exhibit even-mode properties corresponding to the high-order mode. As shown in Fig. 6(c), SSPP waves can propagate through the waveguide efficiently at 10 GHz, which is within the passband. However, the propagation of SSPPs is blocked at 13.5 GHz as shown in Fig. 6(d), which is above the cutoff frequency of the waveguide.
Fig. 6 (a) Top view and (b) bottom view of the fabricated prototype. Simulated z-component electric field distributions of the proposed waveguide with N = 7 at (c) 10 and (d) 13.5 GHz, respectively.
The field confinement capability can be seen from the distributions of electric field amplitudes (|E| = [|Ex|2 + |Ey|2 + |Ez|2]1/2) at 10 GHz and 13.5 GHz along the x direction, as illustrated in Fig. 7. In view of the main central peak at 10 GHz, the electric fields decay sharply when keeping away from central point, showing that the SSPP modes are tightly confined on the surface of the proposed waveguide, while the intensity of the electric fields at 13.5 GHz is remarkably lower than that at 10 GHz. The two insets of Fig. 7 demonstrate the SSPP power flows on the cross-sectional cuts at different locations (i.e., x = 0 mm and 10 mm) along the y direction at 10 GHz. Both of these two insets show similar power distribution and intensity with the same color bar in dB scaling, which implies low propagation loss.
Fig. 7 Simulated amplitude comparisons of the electric field distributions |E| along the y direction between the frequencies of 10 GHz and 13.5 GHz, where x = 0 mm and z = 0.1 mm. The two insets show the power distribution at 10 GHz on the y-z plane when x = 0 mm and x = 10 mm.
Figure 8(a) illustrates the comparisons of numerical and experimental results of the proposed SSPP waveguide with N = 7, where the inset is the top view of the fabricated prototype. Satisfactory agreement in the lower frequency band is obtained, which demonstrates good transmission performance of the SSPP waveguide. The performance of the waveguide fluctuates severely at some frequencies, which is mainly caused by soldering imperfection and connectors. Despite the minor mismatch at the high-frequency band, the measured cutoff frequency is about 13 GHz, which is in accordance with the results from both dispersion analysis and numerical simulations.
Fig. 8 (a) Comparisons between the measured (i.e., Mea.) and simulated (i.e., Sim.) S-parameters of the proposed waveguide when N = 7. (b) Comparisons among the measured S-parameters of the proposed waveguides with different N (i.e., N = 7, 9, 11). The insets in Figs. 8(a) and 8(b) are the top view of the proposed waveguides.
The insertion losses within the passband are mainly caused by the conversion parts design rather than the proposed SSPP waveguide. Figure 8(b) illustrates the measured S parameters of the proposed waveguides with different unit cell numbers (i.e., N = 7, 9, 11) as well as the top view of the three fabricated prototypes (see the inset of Fig. 8(b)). Although the unit cell number of SSPP waveguide is increased from N = 7 to 11, minor changes happen to the insertion losses, which implies that the insertion losses are insensitive to the length of the proposed SSPP waveguide. Hence, the insertion losses of the proposed SSPP waveguide are very low, which manifests high-efficiency propagation of the high-order mode of SSPPs.
5. Conclusion
This work presents a THz high-order SSPP unit cell based on ultra-compact split-ring grooves for the first time with significant area reduction of 83.5% compared to the conventional grounded-slotline SSPP structure. The proposed unit cell greatly improves the operating bandwidth of the high-order mode of THz SSPPs by increasing the high-order mode deviation to the lightline. Then, the prototypes of THz SSPP waveguides using the proposed unit cell are designed and analyzed. To further verify the proposed idea, a similar microwave-band structure is designed with dimensions scaled up, where the mode conversion between traditional guided wave and SSPP wave is achieved by directly connecting microstrip line to the proposed SSPP waveguide without gradient transition structure. Thus, the longitudinal and transversal dimensions of the whole circuits will be potentially reduced due to such conversion-free structure with the design process highly simplified. The measured results agree with the simulated ones validating the proposed idea. This work is very promising for the development of plasmonic integrated circuits at microwave/THz frequencies.
Funding
National Natural Science Foundation of China (61601390); Natural Science Foundation of Guangdong Province (2016A030310375); Shenzhen Science and Technology Innovation Commission (JCYJ20170306141249935).
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