Single-conductor co-planar quasi-symmetry unequal power divider based on spoof surface plasmon polaritons of bow-tie cells

In this paper, the spoof surface plasmon polaritons (SSPPs) transmission line (TL) of periodical grooved bow-tie cells is proposed. The complex propagation constant and characteristic impedance of the SSPPs TLs and microstrip lines (MLs) are extracted using the analytical method of generalized lossy TL theory. The properties of the SSPPs TLs with different substrates and the same geometrical configuration are experimented. Then, for comparison, two ML counterparts are also experimented, which shows that the SSPPs TL is less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, compared with the ML ones. The single-conductor co-planar quasi-symmetry unequal power divider based on this SSPPs TL is presented in microwave frequencies. For experimental validation, the 0-dB, 2-dB, and 5-dB power dividers are designed, fabricated, and measured. Both simulated and measured results verify that the unequal power divider is a flexible option, which offers massive advantages including single-conductor co-planar quasi-symmetry structures, wide-band operation, and convenient implementations of different power-dividing ratios. Hence, it can be expected that the proposed unequal power dividers will inspire further researches on SSPPs for future design of novel planar passive and active microwave components, circuits and systems.

In this paper, the spoof surface plasmon polaritons (SSPPs) transmission line (TL) of periodical grooved bow-tie cells is proposed. The complex propagation constant and characteristic impedance of the SSPPs TLs and microstrip lines (MLs) are extracted using the analytical method of generalized lossy TL theory. The properties of the SSPPs TLs with different substrates and the same geometrical configuration are experimented. Then, for comparison, two ML counterparts are also experimented, which shows that the SSPPs TL is less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, compared with the ML ones. The single-conductor co-planar quasi-symmetry unequal power divider based on this SSPPs TL is presented in microwave frequencies. For experimental validation, the 0-dB, 2-dB, and 5-dB power dividers are designed, fabricated, and measured. Both simulated and measured results verify that the unequal power divider is a flexible option, which offers massive advantages including single-conductor co-planar quasi-symmetry structures, wide-band operation, and convenient implementations of different power-dividing ratios. Hence, it can be expected that the proposed unequal power dividers will inspire further researches on SSPPs for future design of novel planar passive and active microwave components, circuits and systems. © 2016 Author(s). All

I. INTRODUCTION
Surface plasmon polaritons (SPPs) are waves that propagate along the metal's surface due to the interaction of free electrons and photons in the field of optics, which has been explored extensively in subwavelength optics, data storage, microscopy, and biosensor. 1 Despite metals are presented as perfectly electric conductors (PECs) instead of plasma with negative permittivity at lower frequencies, the mimicking surface plasmons or spoof surface plasmon polaritons (SSPPs) propagating along a perfectly conducting surface can also be achieved by drilling an array of holes or corrugating with a periodic array of radial grooves. 2 SSPPs have been performed over the last years, [4][5][6][7][8][9][10][11] in which SSPPs are structured by ML with periodic  holes, corrugated metal surface with underlayer metal, complementary symmetric grooves, combshaped cells, etc. For characterizing the SSPPs, equivalent circuit model of SSPPs unit cell 12 and  analysis of loss feature about the SSPPs TL based on the perturbation method 13 are already proposed, nevertheless, extraction of the complex propagation constant and the characteristic impedance is still an inevitable obstacle in further expanding the range of SSPPs applications. Recently, numerous researches on a wide range of components or devices utilizing SSPPs have been reported. In order to achieve frequency-selective SSPPs in the microwave and terahertz frequencies, high performance wideband filters exploiting the high confinement property of the SSPPs mode have been proposed, [14][15][16] and tunable rejections can be achieved by adding electrically resonant metamaterials near the SSPPs TL. 17 Additionally, directional couplers, 18-20 power dividers 18,21 and feeding network for the antenna array 22 have been designed. It is suggested that the SSPPs have enormous potential of building such a circuit or system at lower frequency bands. However, to the best of our knowledge, there are no published reports on unequal SSPPs-based power dividers with flexible power-division ratios, which will be necessary in asymmetric power amplifiers, 23 passive and active antenna arrays, 24 high-performance radar front-ends, 25 etc. Therefore, the development of novel unequal SSPPs-based power dividers is prior to the implementation of the SSPPs-based microwave front-ends including power amplifiers and antenna arrays.
In this paper, the SSPPs TL of periodical grooved bow-tie cells is proposed. The complex propagation constant and characteristic impedance of the SSPPs TLs and MLs are extracted using the analytical method of generalized lossy TL theory. The properties of the SSPPs TLs with different substrates and the same geometrical configuration are experimented. For comparison, two ML counterparts are also experimented, which shows that the SSPPs TL is less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, compared with the ML ones. Then, we present a single-conductor co-planar quasi-symmetry unequal power divider with different power-dividing ratios. For experimental validation, the 0-dB, 2-dB, and 5-dB power dividers are designed, fabricated, and measured. Both simulated and measured results show that the SSPPs-based unequal power dividers offer several advantages: 1) single-conductor co-planar quasi-symmetry structures, 2) easy implementations of different power-dividing ratios, 3) wide-band operation (3-8 GHz and almost the fractional bandwidth of 91%), and 4) the external performances are less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency. Therefore, it can be believed that the proposed SSPPs-based unequal power divider will be a flexible alternative for controllable output power division and it will play an important role in further developments and applications of SSPPs-based circuits and systems in microwave and terahertz frequencies.

II. DESIGN OF SSPPS TL
One of the important features of SSPPs TL is SSPPs waves can propagate along the periodically structured metal surfaces in microwave frequencies. The propagation characteristics of the SSPPs can be controlled by the metal geometry, such as array of drilled holes, 2,9 periodically corrugated metal surface, 4-7 complementary symmetric grooves, 8 and trapezoidal grooves. 10 In this paper, the SSPPs TL of periodical grooved bow-tie cells with easy adjustment of more parameters, enhanced confinement of surface waves on the two edges of the symmetrical bow-tie metallic cells, and flexibility of building power dividers is proposed. The proposed single-conductor SSPPs TL of 20-unit bow-tie cells is depicted in Figure 1(a). The waves propagating along the SSPPs TL are realized using bow-tie cells, and broadband transition with quarter elapse and gradient SSPPs line is used to achieve high-efficiency conversion between coplanar waveguide (CPW) and SSPPs TL.
In the proposed bow-tie cell, the widths (c 1 and c 2 ), depth (l 3 ) and length (w 3 ) of a side of the void square have major influence on the dispersion relations and confinement ability of SSPPs waves. The dispersion curves of the SSSP unit cells with different parameters and MLs on substrates FR4 and Di880, which are solved by the eigenmode solver of CST Microwave Studio, are plotted in Figures 1(b) and (c). When c 1 = 2 mm, c 2 = 2 mm, w 3 = 0 mm, and l 3 = 4 mm, the bow-tie cell becomes normal H-shaped structure in Refs. 3,11,16,17,19-21. As shown in Figures 1(b) and (c), TL at 5 GHz and 7 GHz. It can be seen that high confinement of the electric energy on the surface and two edges of the symmetrical bow-tie metallic cells is realized.

III. ANALYSIS of SSPPs TLs and MLs
For comparison, we fabricate several SSPPs TLs with different numbers of bow-tie cells and MLs on two different types of substrates. The measured scattering parameters of 20-, 25-and 30-cells SSPPs TLs are in good agreement with the simulated results from 3 to 8 GHz, as shown in Figures 3(a), (b) and (c). Note that the proposed SSPPs TLs are less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the frequency of 8 GHz compared to the ML in Figure 3. The numbers of unit cells (i.e. different length) and substrate types of SSPPs TLs have little effect on the reflection and transmission coefficients, namely, S 11 and S 21 , respectively. However, the substrate type of ML has the bigger effect on S 11 and S 21 , as shown in Figure 3(d). This is due to the variation of the characteristic impedance, as a result of the substrate having different thickness and dielectric constant. Compared to the simulated results, the measured S 11 and S 21 of MLs change obviously within the operating frequency, because both the dielectric constant and dielectric loss vary with the frequency. Therefore, if the proposed SSPPs TLs are applied to the microwave components, circuits, and systems, they will have a special and inherent feature, namely, the external performances are less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency.
The attenuation phenomenon is one of the important features of the SSPPs TLs, thus the generalized lossy TL theory is utilized to represent the properties of the two-port single-conductor co-planar SSPPs TLs accurately. Unlike the lossless TL theory, the generalized lossy TL theory is widely applied in microwave engineering. The complex propagation constant γ and the characteristic impedance Z C can be determined by the following equations: 26,27  where S ij(=1,2) can be the simulated or measured scattering parameters while α, β, R C , X C , R 0 , and L are the attenuation constant, phase constant, real and imaginary parts of the characteristic impedance, the port impedance, and the length of TL, respectively. It can be observed from Figure 4(a), the predicted attenuation constant α of FR4-based SSPPs TL is much smaller than that of FR4-based MLs. In addition, although the used substrates change from Di880 to FR4 for SSPPs TL, the variations of attenuation constant α and phase constant β of the SSPPs TLs are less obvious than MLs from 3 to 6 GHz. Figure 4(b) shows the complex characteristic impedance (i.e., the real part R C and the imaginary part X C ) of SSPPs TLs and MLs with the substrates  of FR4 and Di880. Similarly, compared to MLs, the variations of complex characteristic impedance of SSPPs TL are less obvious when two different substrates are applied.

IV. DESIGN of SSPPs-BASED POWER DIVIDERS WITH VARIOUS UNEQUAL POWER DIVISIONS
According to the coupled mode theory, when two waveguides with the same propagation constant are placed adjacently, the electromagnetic energy can be efficiently coupled from one waveguide to another. Therefore, it is hopeful to design a power divider with different power-dividing ratios by constructing symmetry or quasi-symmetry structures. The single-conductor co-planar power divider with different power-dividing ratios using the proposed SSPPs TL is presented. The design procedures of the unequal power dividers can be summarized as follows. 1) Determine the operating frequency and the cutoff frequency. Choose the values of dielectric constant, thickness, and loss tangent of the material substrate. Then, determine parameters of the bow-tie cell according to dispersion curves. 2) Determine the number of SSPPs cells, and design the broadband transition for high-efficiency conversion between the CPW and SSPPs TL. 3) Duplicate and rotate one-half of the SSPPs TL along the z-axis, and determine the size of two interfaces connecting input and output (the core part of the power divider). 4) Simulate and measure the total scattering parameters of the proposed power divider.
In order to demonstrate the flexible unequal power-division feature of this proposed power divider, three cases with different power-division ratios are designed and fabricated on FR4. The schematic configuration of these power dividers are depicted in Figure 5. Figure 5(a) shows the diagram of equal power divider case, one-half of 20 unit cells SSPPs TL ( Fig. 1 (a)) of length d = 80 mm is duplicated and rotated the angle θ of 150 o along the z-axis, and cut by the blue dashed triangle to divide the electromagnetic energy into two outputs. By cutting the blue dashed trapezium T and changing the shape of the blue dashed triangle, different power-dividing ratios or coupling coefficients of the proposed SSPPs-based power divider are obtained. The core parts of the 0-, 2-, and 5-dB power dividers are shown in Figures 5(b), (c) and (d). It can be seen from the Figure 6 that flexible alternatives for output power division are achieved and the measured power-division ratios are about 0, 2 and 5 dB, respectively. The measured results verify that the implementations of different power-dividing ratios of the proposed SSPPs-based power divider using a single-conductor co-planar quasi-symmetry structure can be easily and conveniently accomplished, which is essentially different from the ML-based unequal power dividers. 28 In addition, simulated and measured results show that the proposed SSPPs-based unequal power dividers can provide wide-band operation and the operating 10 dB return-loss band is about from 3 to 8 GHz (i.e. the fractional bandwidth is almost 91%).

V. CONCLUSIONS
In summary, we have proposed a new single-conductor co-planar SSPPs TL with novel periodical grooved bow-tie cells for the first time. By utilizing the generalized lossy TL theory, the complex propagation constant and characteristic impedance of the SSPPs TLs are effectively and conveniently extracted to analyze the lossy feature of the proposed SSPPs TLs. We also compare the properties of the SSPPs TLs and MLs with two different substrates in the case of the same geometrical configuration. We further verify that SSPPs TLs are less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, which is a clear advantage. Finally, a novel single-conductor co-planar quasi-symmetry unequal power divider based on the proposed SSPPs TL is investigated. The key advantages of the proposed SSPPs-based unequal power dividers include (i) the external performances are less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, (ii) single-conductor co-planar quasisymmetry structures, (iii) wide-band operation (the fractional bandwidth of 91%), and (iv) simple implementation of different power-dividing ratios. We show that different wide-band power-dividing ratios of the SSPPs-based power divider can be readily designed and implemented using a singleconductor co-planar quasi-symmetry structure, which would lead to future implementation of other novel single-conductor co-planar passive and active microwave components, circuits and systems based on the SSPPs TLs.

VI. METHODS
Numerical simulations of SSPPs TLs and E-fields are performed by the commercial software Ansoft HFSS, and dispersion curves are performed by the commercial software CST Microwave Studio. Two types of substrates FR4 and Di880 are chosen for the simulation model and experimental