1. Introduction

Terahertz (THz) waves have attracted extensive attentions and have been intensively investigated because of their promising applications in fields such as imaging, communication, sensing, chemical testing, security check and healthcare [1]. One of the major obstacles for the development of THz technology is the difficulty it manipulating THz waves. There are two basic methods for routing THz waves, i.e., the quasi-optic approach and the guiding structures approach. People resort the former to beam focusing and free space propagation, but in the latter THz waves are confined within a waveguide. The waveguides have obvious advantages to form integration and compact size. Therefore, efficient waveguides and their functional devices are favorable for the development of compact and highly integrated THz systems.

Planar metallic waveguides, common transmission lines at microwave and millimeter wave frequencies, have many favorable properties such as small size, low fabrication cost, and ease of integration, leading their potential use in THz regime. However, in the planar waveguides, the substrate thickness is comparable with the operation wavelength, in which Cherenkov radiation is inevitable [2,3 ]. As a result, the THz waves suffer from unacceptable radiation loss when they propagate along the interface between the metallic waveguide and its substrate. Although this problem can be solved by using homogenous medium or layered medium as their substrates [4], the complexity is increased significantly.

Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves originated from the collective oscillations of electrons at the interface between a metal and a dielectric in optical frequencies [5]. The highly-localized feature of SPPs makes it possible to overcome diffraction limit and realize highly integrated circuits and devices in the areas of optoelectronics, material science, and biosensing [6–8 ]. In THz and microwave regimes, however, the natural SPPs don not exist because metals in these frequency bands behave like a perfect electric conductor (PEC). Recently, Pendry et al. presented a plasmonic metamaterial that is formed by decorating periodic arrays of subwavelength holes or grooves on metal surfaces, which provides a way to artificially control SPP mode [9,10 ]. For mimicking the characteristics of the SPPs in optical frequencies, the surface waves supported by the structured metal surfaces are also named spoof SPPs (SSPPs). Nevertheless, these early plasmonic metamaterials have a major limitation in applications in the integrated circuit due to their inherent three dimensional (3D) geometries [10–14 ]. To solve the problem, planar plasmonic metamaterials have been proposed [15–20 ], which pave the way of developing versatile surface wave integrated devices or circuits at lower frequency bands, especially at terahertz regime. Based on the planar plasmonic metamaterials, high performance THz waveguides and their functional devices have been developed [16].

To further expand the application areas of planar plasmonic metamaterials, we propose an ultra-wideband 3-dB power divider based on a straight plasmonics waveguide having composite structure and two branch waveguides with H-shaped structure. By choosing suitable structure parameters, the SSPPs waves supported by the straight plasmonic waveguide have similar dispersion relation and mode characteristic to the ones confined by the branch waveguide. Attributing to these features, the SSPPs waves propagating along the straight waveguide are equally divided into two parts by the two branch waveguides with high efficiency. To demonstrate the performance of the THz power divider, we fabricate the power divider in microwave frequency by scaling up their geometric structure dimensions. The measurement S parameters show excellent performance in a wide frequency band.

2. Transmission and mode characteristics of Y-splitter

Figure 1(a) illustrates the schematic of the Y-splitter which consists of a straight waveguide and two branches. The two branches acting as output terminals are formed by periodically arranging the H-shaped structures. Furthermore, the H-shaped structures in the two branches have the same structure parameters. The straight waveguide is input terminal, which is a periodic array of a composite H-shaped structure formed by opening air holes in the middle of H-shaped structure. In order to decrease reflection, the two branches are respectively connected with the straight waveguide by a curved waveguide along a circular arc of radius$R=2.9mm$, and the center angle of the arc is set as$\theta ={21}^o$. As shown in Fig. 1(a), the golden area represents the Y-splitter which is formed by decorating grooves or holes in the metal ($\sigma =5.9\times {10}^{7}S/m$) stripe with thickness of 0.7$\mu m$, and the blue part is dielectric substrate whose thickness and relative dielectric constant are$11\mu m$and 3.38, respectively.

 

Fig. 1 (a) The schematic of the plasmonic Y-splitter, and the details of H-shaped structure and composite H-shaped structure. (b) Dispersion relations of the H-shaped structure and composite H-structure, where the red and green solid lines correspond to the H- and composite H-shaped structures, respectively. The dashed black line denotes the light line. (c) The simulated E _z distributions of SSPPs waves supported by the composite H-structure at 0.83THz. (d) The simulated E _z distributions of the H-shaped structure at 0.83THz.

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In the proposed plasmonic waveguides, the period (d) and depth (h) of grooves have major influence on the cutoff frequencies of the dispersion relations of SSPPs wave, whereas the groove width (a) mainly affects the confinement ability of SSPPs wave. Therefore, we first choose the cutoff frequencies such as 0.8THz from which we can decide the parameters d and h by optimization method. Furthermore, the parameter a is chosen to obtain a stronger field confinement. According to the above explanation, the parameters of the two kinds of plasmonic waveguides are finally set as $d=50\mu m$, $a=20\mu m$, $h=50\mu m$ and $b_1=140\mu m$, respectively.

The plasmonic waveguides with H- and composite H-shaped structures can effectively confine the SSPPs waves around their surfaces and make them propagate along the x direction [15,21,22 ]. In order to compare the transmission properties of the SSPPs waves supported by the two plasmonic waveguides, we first calculate the dispersion curves of the SSPPs waves by using the commercial software CST. In simulation, a unit cell of H- and composite H-shaped structures whose material properties are set as PEC is located in an outer air box. The air box has the same size as the periodic cell in the x direction and large enough sizes in the y and z directions. The boundaries of the air box in the x direction are set as master and slave boundaries (i.e. the periodic boundary), and the other boundaries in the y and z directions are set as PEC. Giving phase difference between the master and slave boundaries, we can obtain an eigenfrequency by using the Eigen-mode solver. Changing the phase difference from 0° to 180°, we can calculate all eigenfrequencies. Then, the dispersion relations are obtained.

The simulated results are shown in Fig. 1(b), from which we can observe that the dispersion curves significantly deviate from the light line, implying strong confinement of SSPPs for the two plasmonic waveguides. More importantly, the two plamsonic waveguides have almost uniform dispersion relations, which indicate that the propagation constants (k_x) of SSPPs are equal for the same frequency. According to the coupled mode theory, we know that when two waveguides that have the same propagation constants are placed adjacently, the electromagnetic (EM) energy can be easily coupled from one waveguide to another one [23,24 ]. Hence, it is hopeful to design a high performance Y-splitter by using the two plamsonic waveguides for their similar dispersion relations.

Besides the similar dispersion relations, the consistency of electric field for the SSPPs modes supported by the two plamsonic waveguides is also important to decrease the reflection at the central node of the Y-splitter. To understand the physical phenomenon, we simulate the E _z field patterns in xoy plane 2$\mu m$ above the top surface of the two plasmonic waveguides, respectively, as shown in Figs. 1(c) and 1(d). The observation frequency is 0.83THz which corresponds to the cut-off frequencies of the two plasmonic waveguides. For composite H-shaped structure (see Fig. 1(c)), the electric fields centre on the grooves and the central holes. Furthermore, the E _z field in the central holes keeps the same phase with that in the neighboring grooves. Compared with Fig. 1(d), the E _z fields in the composite H-structure can be looked as combination of E _z fields in two H-shaped structures. For quantitative descriptions, Figs. 2(a) and 2(b) shows the field distributions along the black dashed line shown in the insets. We note that the fields are confined around the subwavelength grooves and cavities and decay exponentially along the two orthogonally lateral (y and z) directions. We further find that the electric fields symmetrically distribute on both side of H- and composite H-shaped structures. The electric fields distributions imply that the SSPPs waves supported by composite H-shaped structure cannot be distorted when they are divided by the two H-shaped structure branches, resulting in very low reflection at the central node of the Y-splitter.

 

Fig. 2 Electric field distributions along the observe line, which is shown by the dashed lines in the inserts, in xy and yz planes, respectively. (a) Field distributions in xy plane. (b) Field distributions in yz plane. The observation frequency is 0.83THz.

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In order to verify the performance of the Y-splitter, we simulate the z-component electric distributions along the surface of the Y-splitter in the xoy plane, as shown in Figs. 3(a) and 3(b) . For comparison, the observation frequencies are chosen as 0.6THz and 0.9THz, respectively, corresponding to two typical frequencies below and above the cutoff frequency of the SSPPs. For 0.6THz, the E _z field propagating along the surface of the composite H-shaped structure is divided equally into the output arms with almost no loss, which demonstrates the good performance of the Y-splitter. Whereas for 0.9THz, the SSPPs field decays quickly along the propagation direction, which implies that the SSPPs wave cannot be confined because its operation frequency is higher than the cut-off frequency.

 

Fig. 3 (a) The simulated E _z distributions of Y-splitter at 0.6THz. (b) The simulated E _z distributions of Y-splitter at 0.9THz.

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To quantitatively evaluate the operation performance of the Y-splitter, we calculate the transmission coefficient. In simulation, three integration planes, such as face1, face2 and face3, are placed at the input and output terminals, as shown the inset in Fig. 4 . The three integration planes can be looked as input and output ports, respectively. Based on this physical model, the transmission efficiency T can be calculated by the formula T ₂₁ = P ₂/P ₁ and T ₃₁ = P ₃/P ₁, where P ₁, P ₂ and P ₃ are the power obtained by integrating the longitudinal component of the Poynting vector in the face1, face2 and face3, respectively. Figure 4 gives the calculated T ₂₁ and T ₃₁, from which we find that the two curves are almost coincident. It indicates that the two output ports get the same EM energy from the input port. Furthermore, we also see that the amplitudes of T ₂₁ and T ₃₁ are about equal to 0.45, which is lightly less than the theoretical threshold (0.5), in the frequency range from 0.15THz to 0.7THz. Based on these characteristics, we conclude that the Y-splitter can divide the input SSPPs waves into two equal output waves in an ultra wideband, and the transmission loss is very little.

 

Fig. 4 Transmission spectrum of the Y-splitter. The inset is the physical model used to calculate the transmission spectrum of the Y-splitter.

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3. Ultra-wideband THz power divider and experimental verification in microwave frequency

Based on the above discussion on Y-splitter, we design a 3-dB power divider, where the SSPPs waves are excited by a coplanar waveguide (CPW) with flaring ground. Figure 5(a) shows the schematic of the proposed power divider, including three CPWs and a Y-splitter. The two CPWs on the right side, which have the same parameters, are used to extract EM energies from the two branch waveguides, whereas the CPW on the left side is used to feed EM waves [21]. As shown in Fig. 5(a), the flaring ground, the gradient grooves and the taper CPW in the regions II, III, IV and V are designed to realize the wave vector and impedance matching between the SSPPs wave in plasmonic waveguide and guided wave in CPW. For the gradient grooves, the groove depth varies from h ₁ = 6$\mu m$ to h ₄ = 24$\mu m$, from h ₅ = 30$\mu m$ to h ₇ = 50$\mu m$, and from h ₈ = 50$\mu m$ to h ₁₂ = 10$\mu m$ with the steps of 0.36$\mu m$, 10$\mu m$ and 10$\mu m$, respectively. When the origin point is placed at P ₁(x ₁, y ₁), the curves of flaring ground in regions III and IV are respectively described as

 

Fig. 5 (a) The schematic of THz ultra-wideband power divider. (b) The S parameters of THz ultra-wideband power divider.

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Figure 5(b) illustrates the simulation results, in which the black solid line is S₁₁ and the red and green lines are S₂₁ and S₃₁, respectively. It can be seen that the S₁₁ is less than −10dB in the frequency range from 0.1THz to 0.75THz, implying high-efficiency conversion from the guided waves in CPW to the SSPPs waves in plamsonic waveguide. On the other hand, the S₂₁ and S₃₁ are higher than −4.3dB in the frequency range from 0.3 to 0.75THz, which is in good agreement with the transmission spectrum shown in Fig. 4. It implies the excellent performance of the plamsmonic power divider in an ultra wideband.

Considering the difficulty of the experiment in THz band, we scale down the working frequency to microwave and design similar devices with scaled geometry. Furthermore, we perform the experiment in microwave frequency to demonstrate the functionality and performance of the proposed Y-splitter. We scale up 50 times the geometric parameters of the designed 3-dB power divider in THz range to make it operate in microwave frequency. The whole structure is constructed on a dielectric substrate (Rogers) whose dielectric constant and thickness are 3.38 and 0.508mm, respectively. The Y-splitter is made of copper film with thickness of 0.035mm on one side of the dielectric plate. Figure 6(a) shows the sample of the plasmonic power divider. The S parameters of the sample are tested by a Vector Network Analyzer (8753ES). In experiments, the third port (port 3) is connected to a matching device when we test the transmission coefficient (S₂₁) for the Vector Network Analyzer having only two ports. By the same method, the S₃₁ can also be obtained. The comparison between the simulation and measurement results are shown in Fig. 6(b). We can see that the simulation results are in good agreement with the measurement ones, except the difference at higher frequency for S₃₁ and S₂₁ curves. From the measurement S₃₁ and S₂₁ curves, we further observe that they are completely coincidence and their maximum reach to −4dB. It shows that the EM energy coupled from port1 can be divided equally to the two output port2 and port3, and hence a high performance plasmonic power divider is demonstrated.

 

Fig. 6 (a) The photograph of the fabricated 3dB SSPPs power divider in microwave frequency. (b) The simulated and measured S parameters of the 3dB SSPPs power divider

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4. Conclusion

In summary, we have investigated the dispersion relations and mode characteristics of the SSPP waves supported by two plasmonic waveguides consisting of composite and single H-shaped structures, respectively. We show that the SSPP waves propagating in the two plasmonic waveguides have similar dispersion relation and mode characteristic. Based on these features, we proposed a Y-splitter, in which the SSPPs waves propagating along the straight waveguide can be divided equally into two parts by the two branch waveguides. Furthermore, we have design a 3dB power divider operating at THz frequency range by employing excitation device of SSPPs. To verify the performance of the power divider, we implemented the experiment in microwave frequency by scaling up the geometry of the device. The measurement results showed very high performance in an ultra-wideband. The proposed plasmonic power divider is helpful to realize other novel planar surface plasmonic devices and circuitry in both microwave and THz ranges.