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Abstract
A bendable transmission line (TL) of spoof surface plasmon polaritons (SSPPs) is presented, which can maintain good transmission performance despite of the deformation caused by bending. Such a TL consists of flexible dielectric substrate and ultrathin metallic strip with zigzag decorations that are designed to support the propagation of SSPPs with strong field confinement and low radiation loss. Furthermore, the proposed SSPP TL is used to excite an amplifier chip efficiently, reaching high and stable gains with nearly no degradation of amplification in the bending states. Numerical and experimental results are demonstrated to verify the bendable merits of both passive TL and active amplifier from 12 GHz to 18 GHz. The flexible and stable characteristics of this design may find utility in novel applications like wearable electronics and conformal plasmonic circuits in the microwave frequencies.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are localized electromagnetic (EM) surface waves that propagate along the metal-dielectric interface in the optical regime. The EM field of SPPs decays exponentially in the directions perpendicular to the interface, and the EM energy is concentrated and significantly boosted close to the contact between metal and dielectric [1–3]. The spoof surface plasmon polaritons (SSPPs) are a sort of surface waves that can imitate SPPs at lower frequencies (e.g., in microwave and terahertz regime) [4–8], and are realizable in plasmonic metamaterials with specially decorated metal surfaces or structures [9–15]. Due to field confinement, designable dispersion, easy fabrication and compatibility with existing circuits, the SSPPs have revealed numerous benefits in microwave and terahertz engineering, including low bending loss [16], reduced crosstalk [17], minimal packing [18], low RCS [19] and higher modes [20], and resulted in a variety of microwave and millimeter-wave devices such as filters [21,22], power dividers [23], amplifiers [24] and antennas [21,25,26].
In the current microwave circuits and systems, the capacity for transmitting signals on conformal surfaces is crucial and highly demanded. There are already devices and circuits that must be incorporated on flexible, bendable, and stretchable substrates, such as biomedical devices [27], deformable light-emitting displays [28], human sensors [29], and artificial skin sensors [30]. In answer to this demand, a variety of flexible TLs have been proposed, among which are mostly based on the microstrip lines. The SSPP TL is a promising candidate of conformal plasma waveguide because its excellent field confinement can result in low radiation loss [18]. Moreover, the SSPPs TL is essentially frequency-selective, and one is able to design the cut-off frequency and group velocity in an easy manner. In addition, the SSPP TLs are well compatible with traditional TLs (e.g., the microstrip line and the coplanar waveguide) when carefully-designed transitions are adopted for good match of momentum and impedance [31–33].
In this study, new types of bendable SSPP TL and amplifier are realized on the flexible substrate and experimentally demonstrated. The zigzag grooves are introduced to strengthen the field confinement of SSPPs [34]. A gradient transition is designed to provide impedance matching between the input microstrip and the zigzag grooves of SSPPs. In experimental tests, the proposed TL demonstrates good transmission performance with nearly no degradation after bending with the transmission coefficient (S21) being consistently above -1.5 dB. The TL is further used to excite an amplifier chip and achieve a gain of nearly 15 dB. Again, despite of bending, the amplifier functions normally and maintains the steady gain. This work applies the merits of SSPPs to flexible microwave circuits, and may have good application prospects in conformal systems and wearable electronics.
2. Design of flexible SSPP TL and amplification circuits
2.1 Design of the SSPP TL
Strong field confinement helps to maintain the transmission performance when the SSPP TL is bent. However, to obtain stronger filed confinement, deeper groove depths and wider line widths are usually required, which leads to a larger size of the circuit. The zigzag grooves can be considered as a folded version of the straight groove, and can effectively solve the conflict between the confinement of EM fields and the miniaturization of circuits. The periodic zigzag grooves have been adopted to compose a TL of SSPPs, and improved field confinement and transmission performance due to the deep-subwavelength structure have been demonstrated [12]. Figure 1(a) depicts the top view of the TL with the total size of 86.5${\times} $20 mm2. The yellow part in the diagram represents the copper with a thickness of 0.018 mm, and the white one is the bendable dielectric substrate of Rogers RT5880 (${\varepsilon _r} = 2.2,{\rm{tan}}\delta = 0.0009)$ with a thickness of 0.508 mm. Because Rogers RT5880 has low loss and high transmission performance in the operating frequency, and is fairly flexible when the thickness is thin, it is chosen as the dielectric substrate in this design. The ground made of copper is also included on the bottom side of the substrate. This SSPP TL is symmetrical and comprises three kinds of sections: the impedance matching section, the transition section, and the TL section, as denoted in the figure, and the lengths of these three sections are L1 = 1.75 mm, L2 = 27 mm and L3 = 29 mm respectively.
Fig. 1. (a) Schematic of the proposed SSPP TL. (b) Details of the impedance matching section. The metal patch is d × s (5 × 1.5 mm2) sized, radius of the through-holes is r = 0.15 mm, period of through-holes is dl = 0.8 mm, and the separation g = 0.2 mm. (c) Details of the transition section with gradient structure. The depth of groove continuously increases from h1 = 0.06 mm to h10 = 0.6 mm. (d) Details of the SSPP unit. The period is p = 1.5 mm, width of the strip is w = 1.5 mm, height of the grooves is h = 0.6 mm (h = 3×y), and width of the grooves is a = 0.2 mm.
The impedance matching sections are located at the two ends, and zoomed out in Fig. 1(b). Here, the 50Ω GCPW ports with multiple metal-ground through-holes are utilized for better stability in the states of bending, stretching or twisting, which commonly happen in flexible electronics. Superior impedance matching from the input to the microstrip is achieved so as to guarantee low reflection and high transmission. Next, the transition section serves to simultaneously achieve impedance and momentum matching between the microstrip and the SSPP structure. This segment includes a gradient tapering structure, which allows the mode of microstrip to be gradually converted to that of the SSPPs. The depth of groove continuously increases from h1 to h10, as is plotted in Fig. 1(c). The last section is the uniform SSPP structure composed of periodic units. In this design, the unit is composed of two-side symmetrical zigzag grooves, as depicted in Fig. 1(d). Folding extent of the zigzag grooves is described by x and y, which are both 0.2 mm here. We denote that a larger folding extent can strengthen the field confinement, but may result in higher dielectric loss and lower transmission, as was discussed in [12]. Therefore, this design is based on a compromise of field confinement, transmission loss, manufacturing accuracy and fabrication cost.
The dispersion characteristics can reveal the theoretical foundation of SSPPs as well as the related phenomena, and hence are carefully investigated in this work. As is known, the SSPPs have an SPPs-alike dispersion relationship but is flexibly designable mainly through the period length and groove of the units. The dispersion curves of the SSPP units in this work are obtained in Fig. 2 through Eigenmode simulations in the commercial software of CST Microwave Studio. On the one hand, as the groove depth h increases, the dispersion curve increasingly deviates from the light line and the cut-off frequency gradually appears, showing the low-pass nature of the SSPPs. On the other hand, the wave vector k of the SSPPs is larger than that of microstrip with the same substrate at the same frequency, indicating that the EM wave propagating on the SSPP TL is a type of slow wave with confined EM fields. In fact, these characteristics are similar to those of the natural SPPs at optical frequencies.
Moreover, it is also observed that the dispersion curve approaches that of the microstrip line as the groove depth h decreases towards 0. Hence, impedance and momentum matching between the SSPP units and the microstrip line can be achieved through the transition section with gradient h from 0 to 0.6 mm, as given in Fig. 1(c). For the uniform SSPP units in Fig. 1(d), the cut-off frequency is about 44 GHz. Therefore, at the target working frequency band of 12-18 GHz, the SSPP TL possesses a good balance between high transmission and strong field confinement. Figure 3 plots the normalized amplitude distributions of the electric field in the cross section when the proposed SSPP TL is in different bending states. It is observed that most EM energy maintains localized to the SSPP structure when the TL is bent more and more heavily, whilst the bending loss and radiation loss are neglectable. In this way, the proposed TL is able to provide high transmission and amplification performance, as will be proved experimentally in the following text.
Fig. 3. The normalized amplitude distributions of the electric field in the cross sections of the proposed SSPP TL. (a) The SSPP TL is flat. (b-d) The SSPP TL is bent and the radius of curvature is (b) R = 200 mm, (c) R = 100 mm and (d) R = 50 mm (see Fig. 9(g) for better understanding of R).
2.2 Design of the amplifier
Figure 4 depicts the diagram of a low noise amplifier loaded in the proposed SSPP TL. The signal is fed through the input port to the SSPP TL, and then to the amplifier through the transition structure. After that, the amplified signal propagates on the SSPP TL again and finally arrives at the output port. In addition, the circuit includes the positive and negative terminals of the amplifier chip and a fan-branch section as a filter capacitor for power supply. This design employs the HMC516 amplifier chip, which has a broad working band with nearly 20 dB gain from 12 GHz to 18 GHz. Wide bandwidth and high gain are the factors that led to its adoption. We denote that the passive part of the circuit is identical to the SSPP TL given above, with all parameters remain intact.
The middle part of Fig. 5(a) shows the amplifier chip and its pins. The SSPP TL is connected to the pins of the amplifier through a trapezoidal tapering structure (as zoomed out in Fig. 5(b)), which is carefully designed for impedance matching. Compared with the gradient impedance matching sections [28–30], this connection is much more compact for the sake of miniaturization of circuits. The length of the trapezoidal transition structure is l = 0.2 mm. The power supply of the amplifier is shown in Fig. 5(c). The VDD pin of the amplifier is led out with a line whose width is wl = 0.15 mm, and afterward to the pin header which is soldered at the circular pad whose inner radius (r1) is 0.52 mm and outer radius (r2) is 1 mm. The size of the pin header and the pad of GND is the same as those of the VDD. Between the VDD and the amplifier chip, there is also a fan-shaped filter capacitor with a radius of rs = 3.2 mm and a central angle of 90 degrees.
Fig. 5. Working principle and schematic of the integrated amplifier model. (a) Schematic of the working principle of the integrated amplifier model. (b) Details of the transition structure between the amplifier chip and the SSPP TL. (c) Details of the VDD and fan-branch section.
3. Results
3.1 Simulation results
To demonstrate the transmission performance of the developed bendable SSPP TL and the integrated amplifier, simulations are performed to compare the scattering parameters (S parameters) when the TL and amplifier are flat and bent to different degrees (with the radius of curvature being 50 mm, 100 mm, and 200 mm, respectively). As shown in Fig. 6, the transmission coefficient (S21) remains approximately -1 dB in all cases, whereas the reflection coefficient (S11) is below -10 dB from 12 GHz to 18 GHz. The simulation results verify that the proposed SSPP TL has great transmission performance, which is maintained with only slight degradation for various bending radii. The amplification effect of the designed amplifier is then simulated and tested as well. Figure 7 demonstrates that the amplifier is effectively activated in the whole frequency range from 12 GHz to 18 GHz, with strong amplification and a gain around 20 dB.
3.2 Experimental results
We manufactured the above designed SSPP TL and integrated amplifier circuit, as depicted in Fig. 8. For fair comparison, we also designed an amplifier fed with the microstrip line, in which the same amplifier chip, line width and length are adopted. For the experiment, three foam cylinders with the radius of curvature being 50 mm, 100 mm, and 200 mm were machined, and the SSPP TL and the integrated amplifier circuits were separately attached to the foam cylinders for testing, as shown in Fig. 9.
Fig. 8. Photographs of (a) the fabricated SSPP TL and (b) the fabricated amplifiers fed with the microstrip line (top) and the SSPP TL (bottom).
Fig. 9. Figure 9. Testing diagram at different radii of curvature. (a-c) The SSPP TL is bent and the radius of curvature is (a) R = 200 mm, (b) R = 100 mm and (c) R = 50 mm. (d-f) The integrated amplifier is bend and the radius of curvature is (d) R = 200 mm, (e) R = 100 mm and (f) R = 50 mm. (g) Radii of the three foam cylinders in (a-c) are 50 mm, 100 mm, and 200 mm respectively.
By affixing the SSPP TL to the cylinders with varying radius, the transmission performance of it was evaluated at various bending curvatures. The experimental results are shown in Fig. 10. It is observed that the SSPP TL maintains great transmission performance in the bending positions with very slight degradation. This is due to the remarkable field confinement ability of the SSPPs, which confines the EM energy to the TL in the sub-wavelength scale.
The amplification performances of the integrated amplifier circuits were then evaluated at various bending curvatures. As shown in Fig. 11(a), the performance of the amplifier excited by the microstrip line degrades gradually as it is bent more intensively. And although there is still amplification observed, the decrease of amplification is about 5 dB in the band from 12 to 18 GHz when the radius of curvature is 50 mm. The performance of the amplifier circuit excited by the SSPP TL, on the contrary, is nearly unaffected at different radius of curvature and the amplification remains almost constant about 15 dB in this frequency band, as shown in Fig. 11(b). In view of this, we conclude that the superior performance of the bendable amplifier is mainly due to the merits of the SSPP TL. To be noted, due to the inaccuracy in manufacturing and assembly, the measured results differ slightly from the simulated ones, but still the good transmission and amplification performance of the SSPP circuits are demonstrated experimentally.
Fig. 11. The measured S-parameters of the integrated amplifier circuit fed with (a) the microstrip line and (b) the SSPP TL.
4. Conclusions
We presented an SSPP TL that can sustain the transmission performance under bending states. Such an SSPP TL has also been used to successfully excite an amplifier chip so as to realize a bendable amplifier with a stable gain about 15 dB from 12 to 18 GHz. Based on the experimental findings, this SSPP based amplifier can maintain the amplification performance on a curved surface, which is a big challenge for the microstrip based amplifier. This designing scheme can be applied in flexible passive and active circuits with advanced performance, and may benefit future conformal and wearable electronics.
Funding
National Key Research and Development Program of China (2021YFB3200502); National Natural Science Foundation of China (61971134, 61631007); Fundamental Research Funds for the Central Universities (2242021R41078, 2242022k30004).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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