Wideband Miniaturized Design of Complementary Spoof Surface Plasmon Polaritons Waveguide Based on Interdigital Structures

In this paper, we present to achieve a broadband miniaturized transmission waveguide based on complementary spoof surface plasmon polaritons (CSSPPs). For this purpose, a novel SSPP design that consists of a corrugated slot line and a group of additional interdigital structures (ISs) is proposed, which brings in an extra solution to control the cut-off property of CSSPPs. The transmission cut-off frequency of the proposed design decreases with the increasing of the number of the ISs. Since the width of CSSPP waveguide is directly related to the operating frequency, the degree of miniaturization can be modulated freely by carefully choosing the number of the ISs. A prototype of device with four-ISs introduced is designed and fabricated. And the cut-off frequency of the design decreases from 10 GHz to 5.3 GHz, when the ISs are added. Experimental results agree well with the numerical simulations. The proposed design illustrates great potentials in modern plasmonic integrated circuits.

of integrated circuits, SSPP modes have become a research hotspot in forming plasmonic circuits. Multi-layer and multi-channel transmissions of SSPP have been proposed 30,48,49 . Co-planar devices have also been discussed in conformal applications 32,50 . Constructing miniaturized design of SSPP becomes an imperative requirement to meet challenges in modern plasmonic integrated circuits.
In this paper, we proposed a novel complementary SSPP (CSSPP) waveguide consisting of a corrugated slot line and a group of IS slabs inside the grooves. The corrugated slot line plays the key role in exciting the SSPP mode and the loaded IS array modulates the cut-off frequency into lower frequency band. The novel design shows properties of high efficiency and better field confinement. In addition, by changing the number of IS slabs, the cut-off property could be shifted in a wide range. A prototype with four IS slabs loaded in the grooves is proposed. The cut-off frequency decreases by 46% compared with that of the traditional CSSPP waveguide with the same widths. The miniaturized CSSPP waveguides show great potentials in the future plasmonic integrated circuits and systems.

Miniaturized cSSpp Design
The schematic structure of a IS-loaded CSSPP waveguide is shown in Fig. 1(a,e). The proposed design is excited via microstrip lines on the bottom, a gradient-varying slot and an eight-unit transition part. The transition part is illustrated detailed in Fig. 1(b). The first five cycles (T1-T5) are five groove structures with different depths for momentum matching. According to the dispersive properties of groove structures, gradually deepened grooves could obtain high efficient excitation of CSSPP mode. Cycles T6, T7 and T8 are grooves with the same depths and increasing numbers of IS slabs, during which further decreases of the cut-off frequencies could be obtained. The main transmission part of the proposed waveguide consists of a main slot and periodically grooves with four IS slabs. Two units of the novel waveguide are shown in Fig. 1(c) with dimensions labeled. The depth D, unit cycle P, and width w of the grooves are optimized to be 5 mm, 4 mm, and 1 mm, respectively. The width w1, length w2 of IS slab, and distance between IS slabs w2 are optimized to be 0.2 mm, 2.5 mm, and 1.25 mm, respectively. The width of the main slot s is 2 mm, and the substrate is F4B with thickness of 0.5 mm and a relative permittivity of 2.65. Designs of Vivaldi antenna in literatures provide good references to achieve excitation of slot lines. The back view of the feeding part is shown in Fig. 1(d), in which the black dashed line represents the slot and circular resonant cavity on the top layer. Signal propagates from the microstrip feeding line to the slot line via field coupling. The length and width of the feeding strip are L0 = 19.5 mm and w0 = 1.28 mm. The circular stub line with radius R1 = 7 mm at the end of the microstrip line improves the coupling efficiency and reduces the reflection. The circular cavity with radius R2 = 4.2 mm helps to improve coupling efficiency and realize unidirectional propagation in slot line. The circular cavity is connected to the main slot via a slot with width widening from 0.2 mm to 2 mm gradually.
As has been fully discussed in literatures 23,27 , the cutoff properties of the SSPP mode in homogeneous media are mainly determined by the depths of grooves. The bigger the depths are, the lower the cutoff frequencies www.nature.com/scientificreports www.nature.com/scientificreports/ would be. Therefore, to realize a lower operating frequency band usually requires a much larger dimension. The appearance of IS slabs enhances the capacitive resonance of the unit cell. The dispersion properties of the proposed structure performed on a homogeneous substrate are studied and illustrated in Fig. 2. The traditional corrugated CSSPP structure is compared with the proposed design with different numbers of IS slabs. One unit of the traditional CSSPP structure is shown in the inset of Fig. 2. The depths keep to be 5 mm, and the traditional CSSPP shows the cutoff property at 10 GHz. When IS slabs are introduced, we observe that the cutoff frequencies of the dispersion curves reduce gradually, which indicates that the momentum matching design of T6-T8 in the transition part is available.
Meanwhile, the dispersion curves of the IS-loaded design deviate more quickly from the curve of slot line, which means that it has a larger wave number. According to basic dispersive model of SPP, where k 0 , k || and k ⊥ are wave number in free space, along and perpendicular to the direction of propagation. For CSSPP mode, it always has relationship of k || > k 0 . The larger the wave number k || is, the larger the imaginary part of k ⊥ would be. And this leads to faster attenuation of field intensity perpendicular to the direction of propagation. Hence, the near-field confinement is enhanced.

Field Analysis and Measurement
Figures 3 and 4 illustrate the simulated 1D and 2D near electric-field distributions to verify the high-performance of CSSPP mode. Near electric field intensity along two reference curves is studied. The coordinate origin is set at the center of the device. The design locates in x-y-plane and the top surface of the metal is set to be at position z = 0. For situation I, the reference curve is along y-direction (from y = −6 mm to y = 11 mm) and in the middle of the substrate in z-direction (z = −0.2 mm). The one-dimensional electric distribution along curve 1 is shown in Fig. 3(a). The blue area marks where the CSSPP structure locates. The positions of the main slot and groove structure are ∈ − y [ 1, 1] 1 and ∈ y [1, 6] 2 , respectively. The black line and blue dashed line in the figure represent field intensity of traditional CSSPP waveguide and the proposed design. For situation II, the reference curve is along z-axis, from z = −2 mm to 2 mm. The one-dimensional electric distribution along curve 1 is shown in Fig. 3(b). The blue area marks where the substrate locates ( ∈ − . z [ 0 5, 0]). From the figure, we can observe that the field is mainly enhanced inside the main slot area, and the proposed design possesses much stronger near field intensity. Thus, the proposed design shows improved near field enhancement.
Another important property of CSSPP mode is the shorter operating wavelength. For CSSPP mode, according to the dispersion properties, we could obtain the equivalent wavelength of the mode through relationship: where D is the cycle of the periodic structures. From data in Fig. 2, we get the wavelength of the design at 4.5 GHz as λ .   Figure 5 shows the S-parameters of the traditional and novel CSSPP waveguides with depths of grooves to be 5 mm. The black solid line and the red dashed line represent transmission efficiencies of both situations, while blue line with squares and orange line with dots represent return losses. The excitation of the design does not support low frequency transmission. The cut-off properties around 1.5 GHz could be seen for both cases. And such cut-off frequencies are mainly restricted by the dimensions of the circular stub line and the circular cavity of the feeding parts. Meanwhile, significant reduction of the cutoff frequencies of CSSPP modes is observed. Moreover, the width of traditional CSSPP structure would enlarge to 10.6 mm to achieve a cutoff frequency of 5.3 GHz. The proposed design occupies less space to achieve a lower operating frequency band.
The photos of the proposed compact CSSPP waveguide are illustrated in Fig. 6(a,b). From the dispersion properties shown in Fig. 2, we can surely conclude that, the more the IS slabs there are, the lower the cut-off frequency would be. Namely a better miniaturization property could be achieved. However, the space in each groove is limited, and the increase of IS slabs leads to undesired difficulties in matching designs. Therefore, a  www.nature.com/scientificreports www.nature.com/scientificreports/ scheme of four IS slabs is chosen for sample. In the experiments, the Agilent Vector Network is used to measure the S scattering parameters via coaxial lines and SMA connectors. The simulated and measured transmissions (black line and red dashed line) and reflections (blue line with squares and orange line with dots) are compared in Fig. 6(c). A traditional CSSPP transmission could be seen and the measured results agree very well with the numerical simulations. It's noteworthy that the area of the metallic surface in the sample is much larger than the slot area. In certain applications, it's feasible to narrow the width of the metallic surface. The transmissions would keep efficient as long as the distances between outer edges and the corrugated slot are not too small. Meanwhile, according to the high-confinement property of CSSPP mode, such design could also be used in conformal applications, even for relatively sharp transitions.

conclusion
A novel CSSPP waveguide consisting of a corrugated slot line loaded with IS slabs is proposed to achieve lower operating frequency band with smaller widths. It has been shown that the novel design has have better ability of near field enhancement and shorter operating wavelength, compared with the traditional CSSPP structures. A prototype with four IS slabs loaded is demonstrated. The cutoff frequency drops to 5.3 GHz without occupying extra space. The miniaturized transmission design could work as the basis of coplanar plasmonic circuits, showing great potentials in the applications of complex and compact plasmonic systems.

Methods
The commercial software, CST Microwave Studio, were used to simulate the transmission, power distribution and return loss of the proposed miniaturized CSSPP waveguide. Eigen-mode calculation was performed to studied the dispersion properties of the unit structures. The sample was fabricated on printed circuit board of F4B, with relative permittivity of 2.65 and loss tangent of 0.001. In experiments, both terminals of the design were connected to the Agilent vector network analyzer via coaxial cables to measure transmission and reflection.