Novel non-periodic spoof surface plasmon polaritons with H-shaped cells and its application to high selectivity wideband bandpass filter

In this paper, one kind of novel non-periodic spoof surface plasmon polaritons (SSPPs) with H-shaped cells is proposed. As we all know, the cutoff frequency exists inherently for the conventional comb-shaped SSPPs, which is a kind of periodic groove shape structures and fed by a conventional coplanar waveguide (CPW). In this work, instead of increasing the depth of all the grooves, two H-shaped cells are introduced to effectively reduce the cutoff frequency of the conventional comb-shaped SSPPs (about 12 GHz) for compact design. More importantly, the guide waves can be gradually transformed to SSPP waves with high efficiency, and better impedance matching from 50 Ω to the novel SSPP strip is achieved. Based on the proposed non-periodic SSPPs with H-shaped cells, a wideband bandpass filter (the 3-dB fractional bandwidths 68%) is realized by integrating the spiral-shaped defected ground structure (DGS) etched on CPW. Specifically, the filter shows high passband selectivity (Δf3 dB/Δf20 dB = 0.91) and wide upper stopband with −20 dB rejection. A prototype is fabricated for demonstration. Good agreements can be observed between the measured and simulated results, indicating potential applications in the integrated plasmonic devices and circuits at microwave and even THz frequencies.

additional structures cause more bulky and larger circuit size. In addition, a flexible dielectric film was introduced to produce frequency-selective SSPPs 23 . The structure is composed of two oppositely oriented single-side corrugated strips coupled to two double-side corrugated strips. Another coupled structure constructed by asymmetric grooved strips can also achieve broadband band-pass response 24 , while its out-of-band suppression was further improved. Besides, the frequency-spectrum-controllable SSPPs were proposed by utilizing coupled SRR particles loaded varactor-diodes 25 . The SSPP fields are cut off at the places where the corresponding SRRs are resonant so that multiple controllable rejection bands can be realized. Recently, a compact wideband plasmonic filter with flat-top transmission response has been proposed 26 , however, its upper stopband rejection level needs to be further improved. Most of above proposed filters feature good in-band transmission characteristic but ignore other important performance indexes such as out-of-band rejection and passband selectivity. Therefore, further performance improvement of the filters based on SSPPs is still required.
In this paper, a kind of novel non-periodic SSPPs loaded with two H-shaped cells in the center of the conventional comb-shaped structure is proposed. The cutoff frequency of the new structure decreases a lot and can be adjusted by changing the parameters of H-shaped cells flexibly. More importantly, the proposed structure not only has wide adjustable frequency range but also can realize better impedance matching. Based on the above design ideas, the spiral-shaped DGS etched on CPW is used to feed the proposed non-periodic SSPPs for filter design. A very narrow stopband response can thus be generated at the edge of the passband at the low frequency, while high selectivity of the wideband bandpass filter can be achieved. The proposed structure is compact without adding other components and has good filtering characteristic, indicating potential applications in the plasmonic integrated circuits and communication systems in the future.

Analysis and Results
Novel non-periodic SSPPs. As shown in Fig. 1(a), a new structure consisting of the traditional combshaped SSPPs and two loaded H-shaped cells is proposed and fabricated on the Rogers 4003 with relative permittivity of 3.38, electric loss tangent of 0.0027. The yellow part is metal (copper) with thickness of 0.018 mm and the grey part is the substrate with thickness of 1.016 mm. The parameters in Fig. 1(a) are set as: l1 = 18 mm, l2 = 25 mm, l3 = 22 mm, and wg = 25 mm. To realize the 50-Ω characteristic impedance at the port, the CPW parameters in Fig. 1(b) are determined as: w0 = 4.6 mm, and g = 0.3 mm. Here, the conversion part from CPW to the traditional comb-shaped SSPPs is composed of the gradient groove and the optimized curve of flaring ground. To obtain the broadband momentum matching, the depth of gradient grooves varies from 0 to 2.1 mm. The function expression of the optimized curve in part II can be described as: where r = y 1 − y 0 = w g . P 0 (x 0 , y 0 ), P 1 (x 1 , y 1 ) in Fig. 1(a) are established coordinates of the start and the end point of function curve. As shown in Fig. 1(c), for the traditional comb-shaped SSPPs, the total width d, the period p, the width of metallic grooves a, and the depth h are chosen as 2.5 mm, 2.5 mm, 1.8 mm, 2.1 mm, respectively. In  Figure 2(a) gives the simulated comparison results between the proposed structure with two symmetrical H-shaped cells and the traditional structure without two H-shaped cells. Obviously, it can be seen that the cutoff frequency decreases about 12 GHz (from 17.3 GHz to 5.3 GHz). Remarkably, the return loss is less than −20 dB in the passband for the proposed structure, implying that better impedance matching is achieved. Figure 2(b) shows that the depth of H-shaped cells h 2 can control the cutoff frequency of the proposed novel non-periodic SSPPs and has little influence on the reflection coefficient |S 11 |. When h 2 uniformly varies from 1.1 mm to 3.1 mm, the cutoff frequency moves to lower frequency. The 3-dB passband bandwidths are 3.62 GHz, 3.32 GHz, 3.02 GHz, 2.72 GHz, and 2.46 GHz, respectively, with the maximum transmission coefficients as −1.09 dB, −1.12 dB, −1.18 dB, −1.34 dB, and −1.52 dB. To obtain flatter in-band return loss, h2 can be determined as 2.1 mm. Besides the good passband performance, the wide and flexible cutoff frequency range is realized by loading compact H-shaped cells instead of increasing the depth of all the grooves.
To further verify the accuracy in the microwave frequency, the fabricated novel non-periodic SSPPs with two symmetrical H-shaped cells is shown in Fig. 3(a) for demonstration. The simulated and measured results are illustrated in Fig. 3(b) with a great agreement. The measured 3-dB passband bandwidth is 73.7% from 2.64 GHz to 5.72 GHz with the operating frequency at 4.18 GHz. The proposed novel structure only has around 1.4 dB transmission loss with the return loss |S 11 | less than −20 dB in the passband, which indicate a good impedance matching between the CPW and the SSPPs. The group delay is less than 0.9 ns in the whole passband. Furthermore, the fabricated non-periodic SSPPs structure has a wideband out-of-band 18-dB rejection from 6.4 GHz to 10.3 GHz.  High selectivity wideband bandpass filter. In microwave circuits design, DGS is usually applied to change the distributed inductance and capacitance of the transmission line so that the band-stop responses and slow-wave characteristics can be obtained 34 . To improve the passband selectivity of the proposed novel non-periodic SSPPs, the spiral-shaped DGS for CPW is firstly introduced to SSPPs filter design. As shown in Fig. 4, a high selectivity wideband bandpass filter is proposed and fabricated on Rogers 4003 with thickness of 1.016 mm. Compared with the structure in Fig. 1(a), only four symmetrical spiral-shaped DGS are added at the input port and output port of the new structure. According to the enlarged view in Fig. 4, the distance between the first spiral-shaped DGS and the port l p is 8 mm and the distance between two spiral-shaped DGS l g is 3.5 mm. The parameters of every DGS are set as: w 1 = 0.25 mm, w 2 = 0.25 mm, l a = 3.25 mm, and l b = 4 mm. In addition, some original parameters are changed: w g = 30 mm, l 1 = 31 mm, l 2 = 28. 5 mm, and l 3 = 9 mm, while other parameters of comb-shaped SSPPs and H-shaped cells in Fig. 4 are the same as those in Fig. 1. The function expression of the optimized curve in part II can be described as: where k is the exponential factor of the curve and here we choose k = 3.2. P 0 (x 0 , y 0 ) and P 1 (x 1 , y 1 ) in Fig. 4 are established coordinates of the start and the end point of function curve, the following conditions should be satisfied: The band-stop effect of the proposed spiral-shaped DGS resonator can be modelled as a parallel RLC resonance circuit shown in Fig. 5(a). As we all known, changing topologies and geometrical dimensions of the DGS  can easily control the equivalent inductance and capacitance of the resonator. Based on transmission line theory and utilization of simulated scattering parameters, the parameters of the resonance circuit for the resonator can be extracted as: where w 0i is the angular resonance frequency, w ci is the 3 dB angular cutoff frequency and Z 0 is the characteristic impedance of the microstrip line. According to the above formulas, the values of the circuit elements are: R 1 = 6.8 kΩ, L 1 = 1.7427 nH, C 1 = 2.566 pF, R 2 = 7.6 kΩ, L 2 = 0.5126 nH, and C 2 = 1.459 pF. As shown in Fig. 5(b), the two resonance frequency f 01 and f 02 of the equivalent circuit agree well with the two transmission zeros near the passband of the proposed wideband bandpass filter. To show the transmission characteristic intuitively, the simulated near-electric-field distributions of the proposed structure at different frequencies are given in Fig. 6.
The frequency points are chosen as 2.4, 4, 5.8 and 9 GHz, which represent the stopband near the first transmission zero, the passband, the stopband near the second transmission zero and the upper stopband, respectively. We can notice that for the stopband shown in Fig. 6(a),(c) and (d), the energy cannot propagate through the center SSPPs structure, while in Fig. 6(b), the energy can propagate intensively and steadily in the passband. The photograph of the fabricated high selectivity wideband bandpass filter and its simulated and measured results of S-parameters are shown in Fig. 7. Obviously, the measured results agree well with the simulated results in Fig. 7(b). The measured 3-dB passband bandwidth is 68% from 2.72 GHz to 5.52 GHz with the operating  frequency at 4.12 GHz. The reflection coefficient is less than −9 dB with the transmission loss around 2.5 dB in the passband. The group delay is less than 0.9 ns in the whole passband. Most importantly, two transmission zeros near the passband at 2.42 and 6.06 GHz lead to high passband selectivity (Δf 3 dB /Δf 20 dB = 0.91). It is widely known that Δf 3 dB /Δf 20 dB is named as square ratio, and it is closer to one, the passband selectivity is better. Meanwhile, the fabricated filter has a wide upper stopband with −20 dB rejection from 5.7 GHz to 10.8 GHz. In addition, the comparison of measured results of our work with previously published reports have been carried out and listed in Table 1. Compared with other wideband bandpass filters based on SSPPs, the passband selectivity of the proposed filter is especially excellent, and more transmission zeros have been realized to improve the upper stopband rejection.

Conclusion
In this paper, a novel non-periodic SSPPs structure is proposed and used for high selectivity wideband bandpass filter design. The non-periodic SSPPs structure is composed of traditional comb-shaped metal strip, two loaded H-shaped cells and CPW transition. Good passband response and impedance matching can be obtained directly, meanwhile its cutoff frequency can be adjusted by the parameters of H-shaped cells flexibly. In addition, the spiral-shaped DGS for CPW is firstly introduced to realize band-stop response on both side of the former passband in the SSPPs structure, and the high selectivity (Δf 3 dB /Δf 20 dB = 0.91) wideband passband filter can be achieved due to the transmission zeros nearby. Both simulation and measurement results have demonstrated the excellent filtering performance for the wideband bandpass filter with the 3-dB bandwidths 68% and wide upper stopband rejection (2.62f 0 ). The proposed novel non-periodic SSPPs and filter provide application potentials to advanced plasmonic functional devices and integrated circuits in both microwave and terahertz frequencies.