We present an experimental study on the bending loss of terahertz (THz) pipe waveguide. Bending loss of pipe waveguides is investigated for various frequencies, polarizations, core diameters, cladding thicknesses, and cladding materials. Our results indicate that the pipe waveguides with lower guiding loss suffer lower bending loss due to stronger mode confinement. The unexpected low bending loss in the investigated simple leaky waveguide structure promises variety of flexible applications.
©2010 Optical Society of America
The study of terahertz (THz) waveguides has attracted growing research interests in the past decade [1–19] and it is a common trend to guide THz waves in dry air for low-loss THz delivery. We recently proposed and demonstrated a low-loss THz air-core pipe waveguide [20,21] for THz waveguiding. The pipe waveguide is the simplest pipe with a large air core region surrounded by thin and low-index dielectric cladding. The structure of the pipe waveguide is shown in Fig. 1 . The THz guiding mechanism in the air-core was found to be the anti-resonant reflection with a leaky mode nature [20–22], while a low attenuation constant on the order of or lower than 0.005cm−1 was successfully achieved. Without complicated metallic coating or multi-layer structures, the pipe waveguides, just like common water pipes and air pipes, are commercially available. The easy availability significantly enhances the practicability of the pipe waveguide. With commercial Teflon pipes, we previously demonstrated that THz waves can be guided in the air-core region up to a distance of 3 meter .
With a leaking waveguiding nature, for future applications of the THz pipe waveguides, it is important to clarify the issue of bending loss. The guiding and bending loss characteristics of simplified hollow-core photonic crystal fiber [23,24], which also supports antiresonant air guiding, have been recently studied. The simplified photonic crystal fiber possesses low bending loss sensitivity for IR band. At the THz regime, the bending losses of bare wires [25,26], subwavelength fibers [15–17], and metal-coated pipe waveguides [27,28] were previously investigated. Sommerfeld waves of a single wire suffer high bending losses , while recent studies indicated that the losses can be reduced by a two-wire structure . The porous subwavelength fibers were found to possess lower bending loss but also higher propagation loss than solid core ones due to improved mode confinement [15,16]. The metal-coated pipe waveguides strongly confine THz waves in the core region and suffer low bending losses [27,28]. Since the pipe waveguides are leaky waveguides, previous results on strongly confined air-core modes cannot be applied.
In this paper, we focus on the experimental aspect of the bending loss of the pipe waveguides. The bending loss is investigated for various frequencies, polarizations, core diameters, cladding thicknesses, and cladding materials. Our result indicates that the pipe waveguides with lower guiding loss also suffer lower bending loss. The unexpected low bending loss in the investigated simple leaky-waveguide-structure promises variety of flexible applications .
In this paper, we are interested in the bending loss of the fundamental guiding mode (HE11). Even though the pipe waveguide is a multi-mode one, higher-order modes suffer much stronger propagation attenuation . That is to say, after propagation in a long-enough pipe waveguide, the fundamental mode will dominate the output power. Figure 2 shows the experimental setup for the measurement of a 100-cm long waveguide. We conducted our experiments with a CW Gunn oscillator module tunable between 320 GHz and 420 GHz. The emitted CW THz waves were directly coupled into the input end of the measured pipe waveguide. We used commercial Teflon pipes (Fluo-Tech Industrial Co., Tao Yuan, Taiwan ) as THz pipe waveguides, and the pipe-output waves were detected by a Golay cell (Microtech Instruments). First, we measured the output power (Ps) of a straight pipe, and then kept the first 30 cm and the last 20 cm of the pipe straight but bent the middle part of the pipe. The position of the Gunn oscillator module was fixed, and we varied the radius of curvature (R) and the location of the Golay cell. After bending, we measured the output power (Pb) again. The bending loss αR is defined as:
3. Results and discussion
First, we investigated the dependence of bending loss on frequencies. The core diameter (D) and cladding thickness (t) of the Teflon pipe waveguide in this experiment were 9 mm and 0.5 mm, respectively. Before measuring the bending loss, we checked the attenuation spectra of the pipe waveguide at first (Fig. 3(a) ). At or near anti-resonant frequencies (about 420 GHz in this case), the pipe waveguide suffers the lowest attenuation and have excellent mode confinement. In contrast, near resonant frequencies (about 336 GHz in this case), the pipe waveguide suffers high guiding loss, since THz waves are hardly confined in the air-core region. We also measured the THz waves by removing the pipe waveguides in the system, and found that the measured power from free space propagating THz waves is lower than 1% of the output power of the pipe waveguides at anti-resonant frequencies. Thus, the THz stray beams hardly affect our experiments. After measuring the guiding loss, we measured the bending loss of the pipe waveguide, and let the polarization of THz waves perpendicular to the bending plane. Figure 3(b) shows the bending loss spectra of the pipe waveguide. It can be found that when operating frequencies are close to the resonant frequencies, the bending loss increases. On the other hand, near the anti-resonant frequencies, bending loss decreases significantly. The plausible argument is that lower guiding loss indicates better mode confinement, thus leads to lower bending loss. Even though the pipe waveguide is with a leaky mode nature, the measured bending loss at the anti-resonant frequencies is unexpected low. When the R = 60 cm, the measured bending loss is about 0.006 cm−1, which is comparable to the bending loss of a strongly confined THz mode in a dielectric pipe with inner metallic coating .
We then investigated the relation between bending loss and the polarization of input THz waves. Since the THz waves generated by Gunn oscillator are linearly polarized and the Gunn module is in a compact size (10 × 5 × 15 cm3), we changed the polarization of the input THz waves simply by rotating the Gunn module. In the experiment, the core diameter and cladding thickness of the Teflon pipe waveguide were 9 mm and 0.5 mm, respectively, and the measurement frequency was 420 GHz. At first, we made the polarization perpendicular to the bending plane, and measured the bending loss for different radii of curvatures. After that, we rotated the Gunn module by 90 degrees to make the polarization parallel to the bending plane, and measured the bending loss again. Figure 4 shows the measured bending loss as a function of the bending radius for two different linear polarizations: perpendicular and parallel to the bending plane. Result shown in Fig. 4 indicates that the bending loss of the pipe waveguide is independent on the polarization of the input THz waves. We also checked the polarization of the output waves before and after bending the pipe waveguides. It was observed that the bent pipe waveguides do not change the polarization of the input THz waves (within the noise level).
Next, we explored the dependence of bending loss on cladding thickness. Figure 5(a) shows the attenuation spectra of two pipe waveguides with different cladding thickness, and it can be observed that 420 GHz and 368 GHz are the anti-resonant frequencies for the pipe waveguide with t = 0.5 mm and t = 1.0 mm, respectively. Both pipes were with the same core diameter of 9 mm. It is found that at anti-resonant frequencies, the pipe waveguide with thinner cladding thickness suffer lower guiding loss, similar to previous reports . That is to say, the pipe waveguide with thinner cladding thickness has better mode confinement than the thicker one. We then measured bending losses at anti-resonant frequencies for each pipe waveguide, as shown in Fig. 5(b). The measurement result indicates that the thinner pipe waveguide suffers lower bending loss, once again attributed to stronger mode confinement.
Figure 6 shows the result of the further measurement regarding the relation between bending loss and core diameter. We measured the bending loss of pipe waveguides with 7 mm and 9 mm of core diameters. The cladding thickness was kept the same (t = 0.5mm), and the operating frequency was 420 GHz. When the bending radius of curvature is large enough, the measured bending loss of the wider pipes is similar to that of the smaller pipes. However, as the bending radius decreased, we found that pipes with a wider core size suffer lower bending loss. Since pipes with a wider core diameter possess lower guiding loss and have better mode confinement , this result continues to support the previous argument that pipes with stronger mode confinement suffer lower bending loss.
Finally, we compared the bending loss of glass pipes with that of Teflon pipes. Since glass pipes are hard ones, it is hard to bend glass pipes and measure bending loss directly. Thus, we used statistical methods to estimate the bending loss of glass pipe waveguides: at first, we measured the output power of five straight glass pipe waveguides, and Ps is the average value of the output power. We also had two bent glass pipes with R = 60 cm and one bent glass pipe with R = 75 cm, and measured Pb from them. Figure 7(a) shows the measured attenuation spectra of Teflon and glass pipe waveguides. At the anti-resonant frequencies (364-368GHz), the attenuation constant of straight glass pipes is about 0.01 cm−1, and that of the straight Teflon pipes is slightly lower than 0.01 cm−1. That is to say, Teflon pipes provide better mode confinement of THz waves. Figure 7(b) shows the bending loss measurement for two different pipes. The measurement results indicate that glass pipe waveguides suffer greater bending loss than Teflon pipe waveguides. Once again, we found that the pipe waveguides with lower guiding loss encounter lower bending loss.
In conclusion, bending loss of leaky-mode pipe waveguides is investigated for different frequencies, polarizations, core diameters, cladding thicknesses, and cladding materials. It is observed that bending loss is independent on the polarization of THz waves. Experiment results indicate that, to have a low bending loss, pipe waveguides with a large core diameter and a thin cladding thickness are desired. At or near anti-resonant frequencies, the pipe waveguide also suffers lower bending loss. All different experiments support that those pipe waveguides which possess lower guiding attenuation also possess lower bending loss, attributed to stronger mode confinement. Our investigation indicates that even though it is with a leaky mode nature, the dielectric pipe waveguide holds not only magnificent flexibility but also possess unexpected low bending loss. It is expected that these easily available, low loss, and low bending loss THz pipe waveguides would have a high potential for THz sensing, communication, and imaging applications [30–32].
This work was sponsored by the National Science Council of Taiwan (NSC) under grants NSC96-2628-E-002-043-MY3, NSC99-2120-M-002-013 and NSC97-2221-E-002-047-MY3.
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