Transmission Characteristics of Flexible Low-Loss Solid Circular Polymer Dielectric Waveguides for Sub-THz Applications

This work investigates transmission characteristics of flexible solid circular polymer dielectric waveguides (SCPDWs) in the sub-THz band, especially those important for practical applications, including transmission loss, energy confinement, and bending loss. In addition, the expanded polyethylene (EPE) cladding and interconnector are introduced to ensure good working conditions and facilitate extended transmission length, respectively. The 1.5-mm-diameter SCPDW made of properly selected PTFE with low loss is considered and investigated in detail. The simulation shows that more than 99% power can be confined in the 9-mm-diameter circular area when the frequency is over 90 GHz. The prototypes are fabricated and measured within 88–140 GHz. The measurement shows that the PTFE SCPDW features low loss of 0.5–4.8 dB/m. A 30-mm-radius 90° bending is generally lossless in frequencies over 120 GHz, and adopting the polarization orthogonal to the bending direction can reduce the bending loss. A 9-mm-diameter EPE cladding brings about 1 dB/m attenuation, which, however, dramatically reduces external interference on the PTFE SCPDW. The designed interconnector can easily extend the SCPDW transmission length with an acceptable loss less than 2 dB. The above results prove that the PTFE SCPDW and its corresponding cladding and interconnector can achieve good sub-THz high-speed wired interconnects. Though only a specific diameter is considered, the performances of SCPDWs with different diameters can also be expected. With the above features, the proposed SCPDW indicates a good candidate for building short-distance high-speed wired communication systems in the sub-THz band.


Introduction
Due to the data transmission requirements for high-speed interconnects and largecapacity communication systems, the transmission technology in the sub-THz and THz bands has received much attention in the past few years. The sub-THz transmission technology can be well applied to various application scenarios, such as large data centers (DCs) and high-performance computing (HPC) [1]. At present, electrical and optical interconnects are widely used for these applications but still suffer from some defects. Though low in cost, the electrical interconnect is limited mainly by its inherent ohmic loss at high frequency, resulting in unsatisfactory highfrequency signal transmission and severely impairing transmission data rate. On the other hand, the optical interconnect has the advantages of low loss and wideband. However, it needs electro-optical conversion for circuit connections, which causes low energy efficiency and high cost [2][3][4]. Comparatively, polymer dielectric waveguides (PDWs) feature low cost and low transmission loss in the sub-THz band. Therefore, they are attractive as transmission lines for high-speed wired interconnect applications in the sub-THz band [5,6].
Various PDWs which can be divided into hollow/porous PDWs and solid PDWs (SPDWs) have been proposed and investigated in [5,. Transmission loss is an important property of PDWs and has been studied a lot. The hollow/porous PDWs offer lower transmission loss. There are many works proposed and investigated lowloss hollow/porous PDWs with different polymers and structures [8, 10, 12-14, 17, 19, 21, 23-25, 28]. The measured transmission losses of PTFE hollow circular PDWs were about 2.5 dB/m at 120 GHz in [10,13,14]. Compared with hollow/ porous PDWs, SPDWs are more flexible and easier to fabricate. It has a wide working band and thus has wider applications than hollow/porous PDWs. Nonetheless, SPDWs suffer from higher material absorption losses because of the higher energy confinement [5]. Thus, the choice of polymer material is a key point for SPDWs in achieving low transmission loss and polymer properties investigated in [33,34]. SPDWs with different polymers and structures have been studied a lot [7, 9, 15-18, 20, 26, 27, 29-32]. A rectangular SPDW made of RO3006 (PTFE Ceramic) was predicted to have 44 dB/m transmission loss at 100 GHz [7] and a liquid crystal polymer (LCP) ribbon waveguide was measured to have 23.5 dB/m transmission loss at 140 GHz [18]. Moreover, a solid polyethylene fiber (also belongs to the SPDW) was measured to have 3 dB/m transmission loss at 70 GHz [32] and a solid polypropylene fiber was found to have only 1.39 dB/m transmission loss at 120 GHz [29]. Bending loss is another important property for PDWs in applications. The bending performances of the hollow PDWs made of PTFE were studied with 5 to 25-mm radius bending in [7,10,12,14], and the bending performances of the SPDWs with different radii were mentioned in [16,17,30] and investigated in [31]. However, the effect of polarization on bending is not considered in these works.

3
Besides the characteristics discussed above, cladding for the PDW is also necessary to be considered from the perspective of applications. The air-cladding and microstructured cladding of the PDWs were studied in [5]. However, the former suffers from high losses due to any perturbation to the structure, and the latter is generally rigid due to the large dimension [5]. Thus, from the perspective of mechanical property, they are not flexible. Foamed PTFE with a low dielectric constant was introduced and used as the cladding, and the cladded waveguide was measured to have only 5.5 dB/m loss at 140 GHz [17,35]. However, the particular analyses of the foamed cladding are not given in the works.
From the above discussion, the former works on SPDWs mainly focus on transmission loss and pay less attention to bending loss and cladding, which however are essential to applications. In particular, the bending losses under different polarizations are not considered for SPDWs. Besides, appropriate claddings to provide good working conditions and interconnects for SPDWs also need investigations. To address these issues, this work investigates the transmission characteristics and the corresponding cladding and interconnector of PTFE solid circular PDWs (SCPDWs) with ϕ = 1.5 mm. The studied frequency band ranges from 88 to 140 GHz, covering both the W and D bands. The contributions of this work include as follows: (1) A proper PTFE (with low transmission loss, good formability, and flexibility) is selected to fabricate SCPDWs. Due to the good material property, the PTFE SCPDW has 0.5-4.8 dB/m measured transmission loss within 88-140 GHz, and the transmission loss is relatively low. (2) The impacts of radii and polarizations on PTFE SCPDWs' bending loss are studied in the wide band, and the polarization effect is not considered in the former literature. It is found that adopting the polarization orthogonal to the bending direction can obviously reduce the bending loss. For example, in this work, the 90° horizontal bending with vertical polarization (VP) performs better than with horizontal polarization (HP). (3) The analysis for foamed cladding is conducted with energy confinement. Considering the energy confinement of the PTFE SCPDW (ϕ = 1.5 mm), a 9-mmdiameter expanded polyethylene (EPE) cladding is fabricated to provide physical protection and isolate external interference. The cladding is measured to have about 1 dB/m attenuation, acceptable for most applications. (4) Though only a specific SPDW is considered, guidelines can be concluded for future SPDWs applications.

Theoretical Analyses and Simulations of SCPDWS
SPDWs have more flexible bending and easier fabrication than hollow/porous PDWs, and they are not affected by the resonance or bandgap effect, resulting in a wide working band. Therefore, SPDWs are considered here. In addition, the circular shape features good mechanical properties and is easy to fabricate. Therefore, SCP-DWs are studied in this work.
In regard to the material of SCPDWs, PTFE is considered due to its excellent electrical properties in the sub-THz band [36]. There are different types of PTFE in the industry with varying characteristics for various applications. For fabricating SCP-DWs, PTFE with low transmission loss, good formability, and flexibility is ideal. By experiments, we find that PTFE dispersion resin in accord with HG/T 3028 and ASTM D4895 standards can meet the above requirements well [37,38]. Therefore, the selected PTFE is thus used in this work. Moreover, the diameter of the PTFE SCPDW is set to be 1.5 mm considering the commercial manufacture and simulated performance.
In the following, transmission loss, phase constant, energy confinement, and bending loss under the PTFE SCPDW dominant mode are simulated and analyzed.

Transmission Loss
A section of the PTFE SCPDW is modeled in HFSS 2021 R1 and the dielectric constant r and the loss tangent tan are set to be 2.1 and 0.0003 in the model, respectively. The cross-section of the simulated model in HFSS is shown in Fig. 1. The diameter is ϕ = 1.5 mm, and the distance between the SCPDW and the boundary is set to be D a = 8 mm. Here, to get more accurate simulation results, the free space is divided into 256 evenly arranged grids to increase the mesh fineness. The radiation boundary is used for the model. For calculating the propagation mode and corresponding propagation constant (including phase and attenuation constant), "solve port only" is selected in the driven solution setup corresponding to a 2D EM simulation. The dominant modes of the PTFE SCPDW are two orthogonal HE 11 modes with the same transmission losses and phase constants. Figure 1 shows the two orthogonal HE 11 modes with VP and HP. Through the simulation, the propagation constant of the dominant mode is obtained, and then the transmission loss TL can be calculated as follows: Fig. 1 The cross-section of the PTFE SCPDW model in EM simulation and the E-field vector distributions of the two orthogonal HE 11 modes, including VP (left) and HP (right) where is the attenuation constant and is the phase constant. The attenuation constant is proportional to the dielectric constant r , the dielectric loss tangent tan , the diameter of the SCPDW , and the operating frequency f, as given in below [39]: This indicates that the transmission loss is related to the electrical properties of the polymer material, the working frequency, and the SCPDW's size. Further, the frequency range of single-guided (HE 11 mode) operation for the solid circular dielectric waveguide is given by [39]: where c is the speed of light in vacuum, rs is the dielectric constant of the surrounding space ( rs =1 in this manuscript). Thus, the PTFE SCPDW operates at dominant mode as its dominant mode operation bandwidth is 0-145.98 GHz from (4).
Since the two orthogonal HE 11 are degenerate modes, only one mode is considered in the following. As given in Fig. 2, the PTFE SCPDW's transmission loss and phase constant range from 1.3 to 8.1 dB/m and 1481.4 to 4502.0 rad/m in the 70-170 GHz band, respectively. In particular, the 3 dB/m transmission loss band is from 77 to 114 GHz. The cutoff frequency point c = n 2 (2 f ∕c) (n 2 = 1 for vacuum) for guided and radiation modes supported by the studied PTFE SCPDW is calculated according to [40]. In Fig. 2b, the phase constant of the PTFE SCPDW is close to the cutoff frequency point at the low frequencies. Hence the mode is poorly confined in the frequency band, and the transmission loss is mainly determined by With the frequency increasing, the studied PTFE SCPDW offers better energy confinement (shown later in Section 2.2), and the phase constant is gradually away from the cutoff frequency point. Thus, the radiation loss significantly decreases, and the material loss dominates the transmission loss. The analytical solutions of the transmission loss and phase constant are also given based on the theoretical analysis in [41][42][43]. As shown in Fig. 2, the simulated results of the transmission loss have a good agreement with the analytical solutions in the higher band. The difference in the lower band is because the analytical solution is obtained under the condition without radiation loss. For the phase constant, the analytical solutions and simulated results agree well with each other, verifying the accuracy of the simulations.

Energy Confinement
Energy confinement is defined as the ratio of the transmitted power flowing through the circular area centered at the SCPDW axis over the total transmitted power. In 3D EM simulation, giving the exciting power and integrating the Poynting vector normal to the circular areas with variable diameters, the energy confinements can be obtained. The simulation is conducted with a section of the PTFE SCPDW surrounded by the free space, whose sizes are given in Fig. 1. Then, the energy confinement of the PTFE SCPDW working with HE 11 mode can be obtained.
The simulated complex E-field magnitude distributions of VP HE 11 mode at different frequencies are illustrated in Fig. 3a, indicating better energy confinement for the PTFE SCPDW at a higher frequency. Here, the E-field is the total field rather than a component. Then, the energy confinements for the studied PTFE SCPDW in different circular areas at 90, 120, and 150 GHz are given in Fig. 3b, which are consistent with Fig. 3a. Noting that, for the studied PTFE SCPDW with HE 11 mode, more than 99% of the power can be confined in the 0 = 9 mm circular area at 90 GHz and above. Therefore, when 0 ≥ 9 mm and f ≥ 90 GHz, the studied PTFE SCPDW with HE 11 mode has good energy confinement, and an ideal working condition (low environmental interference) is ensured. Moreover, sensitivity analyses for energy confinement with different waveguide diameters and dielectric constants are shown in Fig. 3c and d. As can be seen, ± 10% waveguide diameter or dielectric constant variation mainly affects the energy confinement at low frequencies. However, when the waveguide diameter is 1.35 mm or the dielectric constant is 1.89, more than 97.6% of the power can still be confined in the 0 = 9 mm circular area at 90 GHz and above.

Bending Loss
The PTFE SCPDW bending model in HFSS is shown in Fig. 4a. The bending section is approximated by multiple segments, and two straight sections are added to ensure the two ports have enough distance to avoid their coupling. 90° bending with different radii and polarizations are simulated and the transmission coefficients, i.e., S 21 , are obtained. By subtracting the simulated transmission loss of straight isometric PTFE SCPDW from the S 21 , the bending loss excluded the transmission loss can be calculated.
The simulated complex E-field magnitude distributions of the 5-mm-radius bending under different polarizations and frequencies are shown in Fig. 4b and c, respectively. The simulated bending losses with different radii and polarizations in the 70-170 GHz band are given in Fig. 4d and e, respectively. Obviously, the 90° bending loss decreases as the frequency and the bending radius increase, because of the better energy confinement at a higher frequency and the larger bending radius causing less structural discontinuity. In particular, the bending loss with a 30-mm radius can be ignored when f ≥ 120 GHz. Comparing the results under VP and HP, we can see that the bending loss under VP has better performance because the PTFE SCPDW can confine the energy better along the polarization's orthogonal direction. As shown in Fig. 4b, the E-field distributions on the cross-section of the waveguide under VP and HP are illustrated, indicating better energy confinement of VP with a horizontal bending direction. Moreover, Fig. 3 Simulated results for a complex E-field magnitude distributions, b energy confinements of VP HE 11 mode supported by the PTFE SCPDW (ϕ = 1.5 mm) at different frequencies, and sensitivity analyses for energy confinement with different c waveguide diameters and d dielectric constants the E-field distributions of the bending show that the PTFE SCPDW under VP can confine energy better in the bending than HP when the PTFE SCPDW lies on the horizontal plane. Then, it can be concluded that adopting orthogonal polarization to the bending direction can reduce the bending loss.

Simulations and Designs of Cladding and Interconnector
Based on the energy confinement analysis of the PTFE SCPDW with ϕ = 1.5 mm, cladding and interconnector are designed to provide good working conditions and facilitate extended transmission length; both are necessarily important for a highspeed wired interconnect system.

Cladding
Environmental interference is usually fatal for practical applications of SPDWs, including SCPDWs. Consequently, claddings with stable chemical and mechanical properties without introducing high losses are considered to ensure good working conditions for SPDWs. Therefore, investigations on the foamed polymer used as claddings are given here. Due to the foamed structure [44], the foamed claddings have dielectric constants close to 1 and extremely low loss tangents. Hence, the dielectric constant is estimated to be 1 to 1.06 (step 0.02), and the loss tangent is set to be 0.0001 to 0.00019 (step 0.00003) in the simulations. From Eq. (4) and analysis in [45], the PTFE SCPDW with foam cladding also operates at dominant mode over the frequency band from 0 to 145.98 GHz with the consideration of core mode. According to the energy confinement analysis in Section 2.3, more than 99% of the power can be confined in the 0 = 9 mm circular area at 90 GHz and above. Therefore, the PTFE SCPDW with the c = 9 mm foamed cladding is modeled in HFSS. The simulation setup is the same as that in Section 2.1, and the losses of PTFE SCPDWs with foamed claddings are obtained through simulations.
According to the simulated results shown in Fig. 5, the loss of the PTFE SCPDW with the foamed cladding increases as the cladding's loss tangent increases, and the loss of the PTFE SCPDW with the foamed cladding in the lower band decreases as the dielectric constant increases. Due to the introduction of the foamed cladding, the energy confinement would be influenced. According to Fig. 6, the E-field distribution and calculated energy confinement are better for the PTFE SCPDW with foamed cladding at 70 GHz, while the impact becomes much less at 90 GHz. Therefore, for the PTFE SCPDW with poor energy confinement in the lower band, the introduction of the foamed cladding improves the energy confinement. As a result, the following two points can be observed. (1) Using foamed cladding can decrease the transmission loss of the PTFE SCPDW in the lower band; (2) increasing the cladding dielectric constant can reduce the PTFE SCPDW transmission loss in the lower band but have little influence on the higher band. Despite the foamed cladding improving the energy confinement, the radiation loss at a low frequency cannot be ignored. Thus, the transmission loss curve of the PTFE SCPDW with foamed cladding has a similar trend to the curve of PTFE SCPDW. From 85 to 170 GHz, the differences between the losses of PTFE SCPDWs with and without cladding are 0.2-1.2 dB, which are the losses caused by the foamed cladding.
To predict the PTFE SCPDW with cladding, bending simulations with a 10-mm radius are carried out with the consideration of mechanical flexibility. As illustrated in Fig. 7, the cladding reduces the bending loss at a low frequency due to the energy confinement improvement, and it contributes a slightly higher bending loss than that without cladding at a high frequency due to the material loss. The difference in the high-frequency band is about 0.8 dB according to the simulation.
Based on the above analyses, the foamed material, EPE, is thus used as the foamed cladding in this work.

Interconnector
To ensure some mechanical flexibility and easy length adjustment for the SCPDW in specific applications and measurements, the interconnect between two SCPDW sections is necessarily important. Thus, an interconnector is designed next for the PTFE SCPDW. As shown in Fig. 8a, the two horns at both sides are designed to realize good impedance matching with a wide band, and the dimension parameters are determined by optimization. The interconnector is made of oxygen-free copper using the high precision computerized numerical control machine (CNC) technology and gold-plated process, as shown in Fig. 8b. Owing to the axisymmetrical structure, the two orthogonal HE 11 modes have the same performances. The simulated performances are illustrated in Fig. 8c, indicating insertion loss is less than 2 dB and S 11 ≤ −15 dB from 88 to 140 GHz. The measured performance will be given in the later section. To verify the performances of the PTFE SCPDW ( = 1.5 mm), the foamed cladding and the interconnector (namely devices under test (DUTs)), waveguide-SCPDW adaptors are designed and discussed firstly. Then, they are used to build a sub-THz SCPDW transmission measurement system. Waveguide-SCPDW adaptors are designed to connect the WR06 or WR10 waveguide with the PTFE SCPDW ( = 1.5 mm). Since two kinds of millimeter-wave vector network analyzer (VNA) extenders (V10VNA2-T/R-A-RLA and V06VNA2-T/R-A-RLA) with WR10 and WR06 waveguides are used to cover the W and D bands, two corresponding adaptors are designed, as shown in Figs. 9 and 10, respectively. The WR10-SCPDW adaptor includes a rectangular waveguide transition, a PTFE-filled circular waveguide, and a horn, as shown in Fig. 9a. For the W band measurement, the WR10-SCPDW adaptor is directly used to connect the WR10 waveguide of the extender with the PTFE SCPDW. For the D band measurement, a WR06-WR10 transition is inserted between the WR06 waveguide of the extender and the WR10-SCPDW adaptor to form a WR06-SCPDW adaptor, as shown in Fig. 10. The adaptors are made of oxygen-free copper using the same process technology of the interconnector. The cutoff frequency of the PTFE-filled circular waveguide shown in Fig. 9a is about 88 GHz, which restricts the lowest working frequency of the system. The simulated performances of the waveguide-SCPDW adaptors are shown in Fig. 9d and Fig. 10b. They are divided into two parts, corresponding to the performances of the WR10-SCPDW and WR06-SCPDW adaptors, respectively. The simulated results indicate that the adaptors work well in 88-140 GHz with S 11 ≤ − 10 dB and S 21 ≥ − 1 dB. As indicated by Figs. 9, 10, and 11, the transitions have a high transmission coefficient and a linear phase response (namely constant group delay). Consequently, the waveguide-SCPDW adaptors cover a large band with low insertion losses in the entire frequency band (88-140 GHz) of our interest.
The sub-THz SCPDW transmission measurement setup consists of a VNA (PNA-X N5245A) with two millimeter-wave VNA extenders, two waveguide-SCPDW adaptors, and DUT, as shown in Fig. 12.

Measurement and Discussion
In this section, the PTFE SCPDW ( = 1.5 mm) transmission characteristics, the EPE cladding, and interconnector performances are investigated by measurements. Note that the experimental facilities limit the upper frequency of measurements, and the lower limit is determined by the waveguide-SCPDW adaptors. Therefore, the measurement frequency ranges from 88 to 140 GHz here.

Transmission Loss, Phase Constant, and Adaptor Losses
Assuming there are n sections of PTFE SCPDWs, S 21 l i is the measured transmission coefficient of the SCPDW with the length l i ( l i+1 ≥ l i , i = 1, 2, 3, …, n). Here, the mean loss of multiple samples is adopted to reduce result variation [46]. Note that the lengths of the PTFE SCPDW samples are different for transmission loss and phase constant measurements. The measurement error of one sample mainly comes from the non-uniform sample dielectric distribution (along with the sample and on its cross-section) and the inaccurate sample length (caused by the deformation and length measurement). Considering the above errors, samples for the transmission loss measurement should be long enough and have enough length differences, and the samples for the phase constant measurement should be short and have small length differences. The detailed explanations for the arrangement are as follows.
(1) For the transmission loss measurement, the selected PTFE has low loss, and thus the loss changes slowly along the sample length (~ 1.3-4.7 dB/m from simulation). If the samples are too short and have small length differences, the change in the measured results caused by the transmission loss may be less than the measurement error, which would lead to inaccurate measured results. (2) For the phase constant measurement, the phase changes fast along the sample length due to high operation frequency (~ 1933.8-3558.1 rad/m from simulation), and the measurable phase is 0-2π. If the samples are too long and have large length differences, the accumulated measured phase error may exceed the measurable phase change between the samples.
Once S 21 l i of different SCPDW samples are obtained, the transmission loss Loss t can be calculated as follows [47]: By sequentially subtracting the measured phases of S 21 l 1 , S 21 l 2 ,…, S 21 l n , the phase change Phase Δl i is obtained. Then, the phase constant can be calculated as follows [47]: Based on the measured S 21 l i and calculated transmission loss Loss t , the measured waveguide-SCPDW adaptor loss Loss c can be calculated as follows: In the measurements, 1, 1.5, and 2 m PTFE SCPDWs are used to obtain transmission and adaptor losses. Two groups of PTFE SCPDW samples with multiple lengths varying from 14.6 to 15 cm and 19.6 to 20 cm, respectively, are prepared for measuring the phase constant, as shown in Fig. 13. Two groups of results can be obtained by measurements, each of which can be used to calculate one phase constant. By averaging the two groups of calculated results, a statistically more accurate phase constant can be obtained. The transmission loss, phase constant, and adaptor loss can be calculated based on the multiple measured results using (5)- (7).
As illustrated in Fig. 14a, the measured transmission loss of the PTFE SCPDW ranges from 0.5 to 4.8 dB/m in 88-140 GHz. In Fig. 14b, the measured phase constant is from 1475 to 3284 rad/m in 88-140 GHz. The measured phase constant shows a discontinuity at 110 GHz because different millimeter-wave VNA extenders are used to cover the W and D bands, introducing measurement errors. The measured and simulated results given in Fig. 14 generally agree with each other. The difference between the measurement and the simulation is from the dielectric constant and loss tangent frequency dispersion [36] and the error of the measurement system. The measured insertion losses of the two waveguide-SCPDW adaptors are shown in Figs. 9 and 10, being 1.3-2.5 dB in 88-140 GHz. The measured result is about ).
1.5 dB higher than the simulated one, which might be caused by the fabrication error and higher ohmic loss. In the design, the adaptor model is made of copper, which is assumed to have an ideal copper conductivity with a smooth surface. However, the conductivity is not ideal and the metal surface has a roughness in practice, thus resulting in a higher ohmic loss than the simulated one. Therefore, the measurement results indicate that the PTFE SCPDW ( = 1.5 mm) has a relatively low transmission loss over the frequency of 88-140 GHz compared with the other reported SPDWs.

Bending Loss
For the sub-THz interconnects, transmission line bending is inevitable. Due to the flexible mechanical property, smooth surface, long length, and relatively small bending radius, it is difficult to maintain a bending with a precise radius in the free space for multiple measurements of the PTFE SCPDWs. Thus, the EPE board is used to fix PTFE SCPDWs with bending. One gap with a uniform depth is etched in EPE board, and PTFE SCPDWs can be well buried inside the board. The EPE board loss for the straight PTFE SCPDW is measured and then used to calibrate the measured bending loss, which is the difference between the measured transmission coefficients of the PTFE SCPDW in free space and buried in the EPE board. The result is shown in Fig. 15, and the measurements are not given in detail here for simplicity. Bending losses of PTFE SCPDWs with different radii and two orthogonal polarizations are considered. The measurement setup is shown in Fig. 16. Here, all the bending angles are 90° for easy comparison. S 21 R i is the measured transmission coefficient of the SCPDW with R i radius (i = 1, 2, 3, …, n) bending, and S 21 T is the measured transmission coefficient of the straight isometric SCPDW. Loss EB is the EPE board loss for the straight PTFE SCPDW, and the fixing length of the EPE board is l E R i , as shown in Fig. 16a. For different radii, the required fixing lengths change, and thus the parameter l E R i has different values. Then, the PTFE SCPDW 90° bending loss with a R i radius, Loss Ri , can be calculated as follows: Due to the low dielectric constant and loss tangent of EPE, the additional EPE board loss for the bending section has little effect on the results, especially in high frequency or with large radius. Therefore, the impact of the EPE board on the measured bending loss is ignored.
For PTFE SCPDWs, the 90° bending losses with 5-, 10-, and 30-mm radii and two orthogonal polarizations are measured. The results illustrated in Fig. 16c and d show that the 90° bending loss with the same radius has a smaller value at a higher frequency. At the same frequency, the bending has a smaller loss with a larger radius. The VP mode generally has a lower bending loss than the HP. These conclusions are consistent with the analyses of the simulations in Section 2.3. As illustrated in Fig. 16c and d, the 90° In particular, the bending loss with a 30-mm radius is less than 0.6 dB when frequency ≥ 120 GHz. Due to the measurement error and low bending loss, the measured bending losses at some frequencies are slightly lower than 0 dB. Compared with the simulated results, the measured bending losses are generally lower than the simulated ones. There may have two reasons for the difference. The first is that there may exist some twisting effect. The second is the inevitable structural deformation caused by bending in practice. Both twisting and bending lead to structural deformation, namely the density distribution change of the PTFE SCPDW at the bending section, which affects the dielectric constant and loss tangent. However, the changes of the electrical property (including dielectric constant and loss tangent) are complex and hard to be obtained and analyzed. Therefore, this phenomenon cannot be precisely modeled in the EM simulation, leading to the difference between simulation and measurement.
To sum up, the measurement results indicate that the PTFE SCPDW (ϕ = 1.5 mm) has acceptable bending loss characteristics. Moreover, to achieve a low bending loss, the SCPDW needs to have a relatively large bending radius and work in a highfrequency band. In addition, adopting the polarization orthogonal to the bending direction is also helpful in decreasing the bending loss.

EPE Cladding
Based on the energy confinement simulations and analyses of the PTFE SCPDW in Section 2.2, more than 99% of the power can be confined in the 0 = 9 mm circular area at 90 GHz and above. Consequently, the PTFE SCPDWs with c = 9 mm EPE claddings are fabricated and measured, ensuring good working conditions for SCP-DWs. The EPE cladding is fabricated by foam injection molding process, and the phototypes of the PTFE SCPDWs with EPE claddings are shown in Fig. 17, indicating good flexibility. To determine its performance, measurements of the EPE cladding loss and bending performance are carried out.
To obtain the transmission loss of the PTFE SCPDW with EPE cladding, the length differences of the PTFE SCPDW and EPE cladding between the two samples should be identical. For all the samples of PTFE SCPDW with EPE cladding, to facilitate the measurements, the PTFE SCPDW has a longer length than the EPE cladding to connect with the adaptors. The measurement and calculation methods are similar to the ones in Part A. Assume that there are m samples, S 21 Ei+1 and S 21 Ei are the measured transmission coefficients of the (i + 1)th and ith samples, and the length difference is l Ei ( l Ei > 0 , i = 1, 2, 3, …, m-1), then the transmission loss of the PTFE SCPDW with EPE cladding Loss EC is calculated as follows: To obtain the transmission loss of the PTFE SCPDW with EPE cladding, the 1-m PTFE SCPDWs with 0.78-m EPE cladding and the 0.72-m PTFE SCPDWs with 0.5-m EPE cladding are measured. For the 10-mm radius bending measurements, the results are obtained from (8) without considering additional EPE board loss owing to the cladding. As shown in Fig. 17b, the measured transmission loss of the PTFE SCPDW with a 9-mm-diameter EPE cladding is from 1.7 to 5.6 dB/m, of which 0.5-1.4 dB/m is the loss caused by the EPE cladding in the band. Compared with the simulations in Section 3.1, the losses caused by the EPE cladding are generally consistent. The electrical properties of the foamed material are related to its porosity, and the degree of porosity is influenced by fabrication [48]. In Fig. 17c and d, the bending loss of the PTFE SCPDW with cladding is about 1 dB higher than that without cladding, showing the agreement with simulations. As mentioned in Section 5.2, the difference between simulations and measurements might come from the twisting effect and structural deformation.
In particular, the PTFE SCPDW with the c = 9 mm EPE cladding is tested when held by a hand or touched by a metal block, fortunately, little impact on the measured results is observed. The phenomenon indicates that most power is well confined within the 0 = 9 mm circular area and the c = 9 mm EPE cladding reduces external interference and ensures good working conditions for the SCPDWs.
Therefore, the PTFE SCPDW with c = 9 mm EPE cladding shows an acceptable loss in the band (88-140 GHz), and it can effectively reduce environmental interference and slightly influence the bending performance with a relatively small radius. Besides, the cladding can provide physical protection for SPDWs without severely reducing their flexibility. Therefore, the EPE material is a good candidate for SPDW cladding in the sub-THz band.

Interconnector
The interconnector is fabricated, as shown in Fig. 8b. To measure the loss of the interconnector, several PTFE SCPDWs with two different lengths l 1 and l 2 (l 2 = 2l 1 ) are prepared. S 21 l 2 is the measured transmission coefficient of the l 2 long SCPDW, and S 21 l 1 +l 1 is the measured transmission coefficient of two l 1 long SCPDWs connected by the interconnector. Then, the interconnector loss Loss in is calculated as follows: Fig. 17 The PTFE SCPDW with the EPE cladding with its a structure, fabricated prototype, and b measured transmission losses, and simulated and measured bending losses of the PTFE SCPDW with and without cladding under c HP and d VP For the measurements, several PTFE SCPDWs with l 1 = 0.5 m and l 2 = 1 m are prepared and measured. The measured Loss in is shown in Fig. 8c, indicating that the loss is less than 2 dB in the whole band (88-140 GHz). The simulated and measured results generally agree with each other.
Obviously, the interconnector has a simple structure and a good performance in the investigated band, which facilitates easily the extended transmission length of the SCPDW.

Conclusions
The transmission characteristics of the PTFE SCPDW ( = 1.5 mm) and its cladding and interconnector have been investigated over the frequency band of 88-140 GHz in this work. Benefiting from the good electrical properties of selected PTFE, the measured transmission loss of the PTFE SCPDW is from 0.5 to 4.8 dB/m in the 88-140 GHz band and is relatively low compared with the reported SPDWs. The 90° bending loss is lower with a larger radius and a higher frequency. Furthermore, the polarization orthogonal to the bending direction helps reduce the bending loss. A 9-mm-diameter EPE cladding is fabricated to eliminate the external interference with a loss ranging from 0.5 to 1.4 dB/m in the band. An interconnector of the PTFE SCPDW is designed and measured, introducing a loss lower than 2 dB. These prove that the PTFE SCPDW and the corresponding cladding and interconnector can build good sub-THz high-speed wired interconnects.
Based on the thorough investigations, some helpful guidelines can be concluded for practical design of SPDWs. (1) Adopting the suitable polymer to make the SPDW is critical to realize low transmission loss, good formability, and flexibility. (2) The polarization direction being orthogonal to the bending direction, working in a high-frequency band, or having a large radius can reduce bending loss. (3) Appropriate foamed cladding can effectively reduce environmental interference while introducing slight loss to SPDWs. These guidelines are beneficial for future SPDWs applications.
Author Contribution Xue and Che conceived the study and designed the measurements. Li and Liao conducted the measurements and data collection. Li and Liao drafted the manuscript, and all authors contributed substantially to its revision. Che takes responsibility for the paper as a whole.

Data Availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.