1. Introduction

Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves which propagate along the interface between metal and dielectric and decay exponentially in the transversal direction in the optical regime [1,2]. In microwave and terahertz (THz) regions, instead of SPPs, only Sommerfeld-Zenneck waves with weak confinement exist because metal behaves as perfectly electric conductors (PECs) with positive permittivity. In order to design SPPs at lower frequencies, plasmonic metamaterials generated by periodic arrays of sub-wavelength grooves or holes have been reported [3–9] which are termed as spoof SPPs (SSPPs) because of the SPP-like features. Moreover, the dispersion relation can be tailored at will by tuning the geometrical parameters. More recently, the energy distribution and loss of SSPPs have also been proposed and studied [10–12]. For accelerating practical applications, the high-efficiency excitation of SSPPs has become a challenging task. SSPPs in Domino structures have been excited successfully by rectangular waveguides [13,14] Nevertheless, the transmission performance at lower frequencies in these structures is unacceptable due to the loose confinement to SSPPs. In addition, the inherited 3D dimensions of these structures seriously limit the practical applications.

Recently, ultrathin corrugated metallic strips with near-zero thickness have been proposed, in which SSPPs can propagate along the surface with long distances in a wide band from microwave to mid-infrared frequencies [15,16]. The conformal surface plasmons (CSPs) are proven to be very promising candidates for planar plasmonic device and circuit applications in microwave and THz regimes [17–19]. However, it is difficult to excite SSPPs efficiently from the traditional transmission lines such as microstrip lines or coplanar waveguides (CPWs) because of the serious mismatch of both momentum and impedance. A broadband and high-efficiency conversion from guided waves to SSPPs was firstly reported [20] to feed energy into and extract signals from plasmonic functional devices through CPWs. More recently, some interesting works have been proposed to smoothly convert guided waves in traditional transmission lines to SSPP waves in plasmonic waveguides [21–30].

As one of the most popular transmission lines, it does make sense to realize smooth transition between CPWs and SSPP structures. However, among the aforementioned works, all the transitions between CPWs and SSPP structures are implemented by a flaring ground based on Vivaldi slot which requires a complicated and time-consuming design procedure. Besides, as can be seen in [20], the transmission performance in the region of low frequencies gets worse because of the weak confinement of SSPPs. In this work, by adding metals on both sides of the corrugated strip as ground plane, a simple and efficient strategy to achieve a smooth bridge between traditional CPWs and SSPP strips is presented. Without requiring flaring ground, the proposed simple transition structure enables easy fabrication and seamless connection with traditional microwave devices. Moreover, the SSPPs are tightly confined in the gap between the strip and ground plane which enhances the confinement ability of SSPP waves, especially for those at lower frequencies whose wave vectors are close to k₀ at the light line. Based on this structure, a plasmonic waveguide with improved low-frequency performance and operating bandwidth is then proposed. Gradient grooves on the corrugated strip are applied to efficiently match the impedance and momentum simultaneously. Furthermore, by etching the two grounds on both sides of the strip with the same periodic grooves symmetrically, tighter field confinement is achieved. Numerical and experimental results validate the high-efficiency matching and propagation of SSPPs in broadband. The proposed waveguides can find potential applications in plasmonic functional devices and integrated circuits in microwave frequencies.

2. Modal analysis

The proposed SSPP strip structure is much like a traditional CPW, except for the periodic grooves decorated on the central strip, as shown in the inset of Fig. 1. The period, width and depth of the grooves are d = 5 mm, a = 1 mm and h = 4 mm, respectively. The dielectric substrate with thickness of t = 0.5 mm is selected as F4B with relative permittivity ε_r = 2.65 and the loss tangent tanδ = 0.003. The thickness of the copper layer over the substrate is 0.035 mm. In order to explore the propagation characteristics of the SSPP strip structure, the dispersion diagram of the strips is firstly calculated by the commercial software CST Microwave Studio as shown in Fig. 1. It has been demonstrated that the symmetric SSPP strips can support both the symmetric mode (even mode) and the anti-symmetric mode (odd mode) of the surface wave propagation [31]. In this work, only the dominant even mode is considered. It is observed that the dispersion curves exhibit the similar feature as that of the same structure without ground on both sides of the strip. All the curves deviate significantly from the light line. Moreover, this departure is greater when ground plane is added which results in a lower asymptotic frequency and tighter EM field confinement, especially in the regime of small wave vectors corresponding to lower frequencies. Furthermore, for the original SSPP strip without ground plane, the SSPP waves at low frequencies have significant radiation loss when propagating along the strip because of weak field confinement, resulting in decreased transmission efficiency. However, the radiation loss can be effectively suppressed by means of adding ground plane on both sides of the strip, which can enhance the confinement ability to SSPP waves and further lead to good enhancement of transmission performance and bandwidth feature.

 

Fig. 1 Dispersion diagram for the dominant surface mode of the proposed SSPP strip with and without ground. The inset is the schematic of the proposed periodic SSPP structure. The line width, gap width, period, width and depth of grooves, width of ground are designed as H = 10 mm, g = 0.4mm, d = 5 mm, a = 1 mm, h = 4 mm and W = 20 mm. The top and bottom copper layers are with the thickness 0.035 mm and separated by a dielectric substrate of F4B (ε_r = 2.65, tanδ = 0.003) with the thickness of 0.5 mm.

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The proposed plasmonic waveguide is illustrated in Fig. 2(a), the sketches of each region are given in Figs. 2(b)-2(d). The length of the three regions are L₁ = 10 mm, L₂ = 40 mm and L₃ = 40 mm, respectively. Region I is the common CPW connected with the SMA connectors. To achieve 50Ω impedance, which is commonly used in microwave circuits, the dimensions of CPW are set as H = 10 mm, g = 0.4 mm and W = 20 mm. Region III, as shown in Fig. 2(d), is the symmetric corrugated strip with grounds on both sides which propagates SSPP waves. The geometry parameters are the same as given in the inset of Fig. 1. As can be seen from the dispersion diagram (Fig. 1), there is a serious momentum mismatch between the common CPWs and SSPP strips, especially when the frequency is close to asymptotic frequency, which will definitely lead to low transmission efficiency. Thus, a transition region is needed to gradually convert the guided waves in CPWs to SSPP waves in SSPP strips. Region II in Fig. 2(c) works as mode conversion section with gradient corrugated strip and the groove depth h varies from h₁ = 0.5 mm to h₈ = 4 mm with an equal step of 0.5 mm.

 

Fig. 2 The schematic configuration of the proposed waveguide. (a) Top view of the structure. Lengths of Region I, Region II and Region III are L₁ = 10 mm, L₂ = 40 mm and L₃ = 40 mm and the thickness of the F4B substrate t = 0.5 mm. (b) Region I: CPW region with H = 10 mm, g = 0.4 mm and W = 20 mm. (c) Region II: Matching transition region with depths of grooves varying from h₁ = 0.5 mm to h₈ = 4 mm with a step of 0.5 mm. (d) Region III: The corrugated strip with ground, in which a = 1 mm, d = 5 mm and h = 4 mm.

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The explanation of the conversion theory for matching procedure of momentum and impedance is demonstrated in Fig. 3. Figure 3(a) shows that the dispersion curve deviates gradually from that of CPW. It can be also observed that the asymptotic frequency lowers step by step when the groove depth h augments. It means that the field is confined more and more tightly with the increase of h. Meanwhile, it can be seen in Fig. 3(b) that the normalized impedance changes from 1 to the impedance of SSPPs strip by using the S-parameter retrieval technique [32] which is a reliable method for planar two-conductor SSPPs structure [26,27]. The impedance shows a gradually increasing trend with the increase of the groove depth. Note that the change rules of impedance of the proposed strip are completely opposite to that of the corrugated strip in [26]. Finally, the proposed transition section realizes both momentum and impedance matching between CPW and SSPPs strip simultaneously and the guide waves can be gradually transformed to SSPP waves with high efficiency.

 

Fig. 3 The transition principle between guided waves and SSPPs with depth h of the periodic SSPP strip increasing from 0.5mm to 4mm by step of 0.5mm. (a) and (b) are the evolution of the normalized wave vector and impedance, respectively.

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3. Miniaturization of waveguide with DGS

To further evaluate the performance of the waveguide quantitatively, a prototype shown in Fig. 4(a) is fabricated and tested. An Agilent E8363B Vector Network Analyzer (VNA) is employed to measure the S-parameters via SMA connectors. Figure 4(i) shows the comparison of simulated and measured responses. It can be seen that the tested results exhibit good agreement at low frequencies, i.e. below 7.2 GHz, which validates the high-efficiency of matching and propagation of the proposed waveguide. The −1 dB and −3 dB insertion loss range from 0 to 3.5 GHz and 0 to 7.9 GHz, respectively. The return loss is almost less than −10 dB from 0 to about 7.2 GHz. However, note that it’s a challenging task to realize good matching in broadband between an SMA connector and a feeding CPW with relatively large lateral dimension. Thus, the measured results become worse gradually above 7.2 GHz, especially near the cut-off frequency (10.4 GHz), due to the serious impedance mismatch caused by soldering imperfections. We believe that the performance of the waveguide in high-frequency region with larger wave vectors will be enhanced by further optimal design with tapers, which will be realized by better connection and matching. Nevertheless, improved low-frequency performance can be achieved as predicted theoretically in the dispersion diagram. In order to get insight into the propagation efficiency of SSPP waves, we also simulate the z-component electric field distributions at in-band frequency 4 GHz and out-of-band frequency 11 GHz, as depicted in Figs. 4(c) and 4(e), respectively. It can be observed that at 4 GHz the guided waves are smoothly converted to SSPP waves and propagate along the surface efficiently. However, in case of 11 GHz which is above the asymptotic frequency, the waves are cut off as predicted. Besides, the z-component electric field distributions at the cross sections A and B (the detailed positions are shown in Fig. 2(a)) of the strip at 4 GHz are illustrated in Fig. 4(g). It can be observed that the fields are confined tightly around the surface which validates the performance of SSPPs.

 

Fig. 4 The measured and simulated results of the performance of the proposed waveguides. (a) and (b) are the photographs of the fabricated prototypes without and with DGS, respectively. (c) and (e) are the simulated z-component electric fields distributions of the waveguide without DGS at 4 GHz and 11 GHz, respectively. (d) and (f) are the simulated z-component electric fields distributions of the waveguide with DGS at 4 GHz and 10 GHz, respectively. (g) and (h) are the simulated z-component electric fields distributions at cross sections A and B of the strip of the waveguide at 4 GHz without and with DGS, respectively. (i) and (j) are the simulated (solid lines) and measured (dashed line) S-parameters of the waveguide without and with DGS, respectively.

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The grounds on both sides of the corrugated strip really provide extra flexibilities to design of plasmonic waveguides. Herein, DGS, which is a very beneficial technique for miniaturization in traditional microwave circuits, is used to further optimize the design. The proposed waveguide with DGS is illustrated in Fig. 4(b). The geometry is almost the same as that in Fig. 4(a) except for the symmetric grooves etched on the two grounds. The use of slot on the ground to generate corrugated CPW has been proposed as a photonic bandgap (PBG) structure and analogous low-pass characteristics have been obtained [33]. The analysis of dispersion characteristics and normalized impedance proposed in this paper can provide theoretical support for the design of the PBG structure with corrugated CPW in Ref [33]. As can be seen in Fig. 1, the dispersion curve deviates further from the light line than that of the same SSPP strip without DGS, which indicates a lower asymptotic frequency and tighter SSPP wave confinement with the same grooves depth. That is to say, size reduction for the waveguide with DGS can be realized due to the decreased cut-off frequency. Moreover, it should be noted that the curves remain almost unchanged for small wave vectors in the dispersion curves. That is to say, better performance in lower frequency range and wider bandwidth can be obtained with enhanced field confinement.

To demonstrate the performance of the proposed waveguide, a prototype with DGS shown in Fig. 4(b) have been simulated and measured. The geometrical parameters of the waveguide are the same as given in Fig. 2. The grooves decorated on each side of ground are symmetric to those on the same side of central strip. Good agreement is obtained between numerical and experimental results in low-frequency band. The curves in Fig. 4(j) show that the waveguide with DGS has a lower cut-off frequency of 9.2 GHz which is in accordance with the dispersion analysis. However, to obtain the same cut-off frequency, the waveguide without DGS requires a deeper groove with the depth of about 4.6mm, which is 15% larger than that of waveguide with DGS. The measured −1 dB and −3 dB insertion loss are in the frequency range from 0.54 to 3.67 and 0 to 7.6 GHz, respectively. We also observe that the return loss is lower than −10 dB from 0.75 to 7.66 GHz. Thus, both tighter confinement and improved performance at low frequencies is verified. In addition, the z-component electric field distributions at in-band frequency 4 GHz and out-of-band frequency 10 GHz are illustrated in Figs. 4(d) and 4(f), respectively, which validate the propagating characteristics. The z-component electric field distributions at cross section A and B of the strip at 4 GHz are shown in Fig. 4(h) as well. Tight field confinement around the surface can be observed.

Compared with common single-conductor SSPPs structures, which own the significance of deep sub-wavelength confinement, low-loss propagation and groundless planar geometry but are still limited by the realization of smooth transition between SSPPs structure and conventional microwave transmission lines with simple structure and high efficiency, the proposed SSPPs waveguide based on corrugated CPW which is a two-conductor structure in this paper can achieve excellent momentum and impedance matching simultaneously with simple configuration resulting in high-efficiency excitation and propagation of SSPPs. The use of flaring ground based on Vivaldi slot structure which is a complicated procedure to design can be avoided. Moreover, the extraction of the normalized impedance of SSPPs structure can be easily realized on the basis of the theory of conventional double-line transmission lines. As is discussed above, the dispersion properties of the double-conductor SSPPs structure are similar to those of single-conductor SSPPs structure except for a greater deviation from the light line due to the enhanced field confinement caused by the effects of adding grounds. More importantly, the low-frequency performance of the proposed waveguides can be improved resulting in a broader operating bandwidth.

4. Conclusion

In conclusion, a plasmonic waveguide propagating SSPP waves is proposed in this paper. A smooth transition between CPW and SSPPs strip with simple geometry and good matching is achieved by adding metals on both sides of the gradient corrugated strip as grounds. Based on this structure, the waveguide can fulfill seamless connection with traditional microwave devices. Moreover, the waveguide with DGS can confine the SSPP waves more tightly on the surface which is realized by etching the ground with the same symmetric grooves. Thus, the proposed waveguide can be miniaturized due to the decrease of the cut-off frequency. Two prototypes are designed and fabricated to validate the designs numerically and experimentally. Measurements demonstrate that good matching and enhanced propagation efficiency in low frequency region are obtained. These results could contribute to applications of plasmonic integrated functional devices and circuits in microwave frequencies.