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Abstract
Flexible gradually tapered metal waveguides (GTMWs) are fabricated by an inner plating silver film in a polycarbonate (PC) capillary for the transmission and imaging at 0.3 THz. It was demonstrated theoretically and experimentally that GTMWs have lower transmission losses and smaller additional losses of bending, comparing with thin constant bore metal waveguides (CBMWs). Measured losses of 1.95 dB and 2.45 dB were obtained for a 1 m long GTMW with bore size varying from 2.6 mm to 1.6 mm under straight and one circle bending configuration. Measured losses were 4.48 dB/m and 7.78 dB/m for 1.6 mm bore CBMW under the same straight and bend configurations. Owing to higher energy concentration at the output, a larger penetration ability of output wave can be achieved by GTMW, which is beneficial for imaging application. A scanning imaging system was established using fabricated waveguides as the probes. Measured results show that the air slits of the order of wavelength can be clearly distinguished. An imaging system with a GTMW probe also has better performances due to lower bending loss and improved coupling efficiency.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz (0.1-10THz) technology has attracted numerous interests in the past decades due to outstanding properties such as high transparency of many important dielectrics and low photon energy, especially important for bio-applications. Terahertz technology is widely used in a variety of applications [1–6], including remote sensing, THz metadevices, and imaging. In particular, imaging using THz wave has attracted much interest due to various important applications in biomedical engineering [7–9], and security control [10,11]. However, most of the THz systems are bulky since they rely on free-space transmission [12]. Thus, the research on a flexible, effective THz waveguide is critically needed in the development of THz technology.
Traditionally, THz waveguides are fabricated by brass, silver, or stainless steel with planar, rectangular, square, or circular cross sections [13]. Such as subwavelength planar plasmonic THz waveguide [14–15] has potential for both passive and active THz guided-wave devices and circuits. Among them, metal or metal/dielectric hollow waveguide [12,16,17] is widely used because of simple fabrication technology, low loss, and flexibility. Meanwhile, researchers found that the attenuation coefficients of gradually tapered waveguide are less sensitive to bending. Daniel et al. [18] proposed a tapered hollow waveguide for CO2 laser light transmission. The waveguides are capable of delivering 15 W of CO2 laser light power. Carlos et al. [19] fabricated silver/silver halide-coated tapered hollow-glass waveguides which are of low-loss, broadband transmission at infrared wavelengths. They found that tapered waveguides are of higher quality output beams than larger constant bore hollow waveguides.
Terahertz imaging includes reflection imaging and transmission imaging. Terahertz reflection imaging has the capability of providing non-invasively surface and depth information about the sample [20]. Dandolo et al. [21] investigated two easel paintings of different ages by 300 GHz waves system. Thickness variations of paint layer and the properties of artistic materials used can be distinguished by analyzing the terahertz image. The transmission imaging system was also widely adopted in THz scanning imaging [22,23] based on the unusual penetration performance of terahertz radiation. Cumis et al. [24] designed a set of confocal microscopes based on a 2.9 THz quantum cascade laser. According to the Rayleigh criterion, lateral and axial resolutions better than 70 µm and 400 µm, were attained.
In order to achieve a high spatial resolution in terahertz imaging, tapered waveguide was usually introduced as probe to obtain a subwavelength aperture at the tip. Hunsche et al. [25] obtained a sub-wavelength spatial resolution better than λ/4 by focusing the THz radiation into a tapered metal tip with a small exit aperture. Liu et al. [26] demonstrated near-field imaging capabilities of a tapered waveguide without cutoff. By properly choosing the output bore size, the concentration of energy, broadband transmission and sub-wavelength spatial resolution can be realized.
In this research, five waveguide samples, two gradually tapered metal waveguides (GTMWs) and three constant bore metal waveguides (CBMWs), were fabricated for 0.3 THz wave transmission and imaging. The attenuation coefficients of modes of GTMW were theoretically analyzed. Contrast with the CBMW counterparts, GTMW provided lower transmission loss and bend loss. Then, waveguide samples were used as probes for transmission scanning imaging system. Measured results showed that imaging system can clearly distinguish the air slits of the order of wavelength. GTMW probes provide better imaging performances owing to low bend loss. Moreover, GTMWs can also effectively improve the robustness of the imaging system due to high coupling efficiency with the THz source. The GTMW is of low loss, flexibility, easy fabrication. It has potential required in a variety of applications, including minimally invasive treatment, terahertz communication, security screening and so on.
2. Theory and experimental system
2.1 Theory
Attenuation coefficients for the waveguide modes are given by Miyagi [27]. In the far infrared and THz regions, the attenuation coefficients of each mode in a 2 T bore size CBMW are as follows.
The above equations can be extended to calculate the attenuation coefficients of GTMWs [28]. The inner bore radius T(z) of GTMW varies linearly along the waveguide as
where L is the length of waveguide, dout and din are the bore radii at the GTMW input and output ends, respectively. Thus, the attenuation coefficient of TE0q mode is obtained by formula (5).In the low-ordered modes, such as TE01, TM11 and TE11, TE01 mode has the lowest transmission loss, followed by TE11 mode and TM11 mode. However, when the THz wave source is linearly polarized, a special coupling system is needed to excite the circular polarization TE01 mode. Moreover, when the waveguide shape is irregular or there is bending, TE01 mode is easy to couple to TE11 mode. Therefore, TE11 mode is usually discussed in metal waveguide.
It can also be concluded from Eqs. (6)–(8) that the attenuation coefficient of GTMW is between that of CBMWs with the same size of large bore and small bore of the GTMW. When the bore size of one end of the waveguide is fixed, the larger the taper of GTMW, the greater the attenuation coefficient is.
2.2 Waveguide samples
Figure 1(a) shows the structure of waveguide samples. Two GTMWs were fabricated. The bore sizes are gradually changed in 1 meter from 2.6 mm to 1.6 mm (2.6-1.6 mm waveguide) and 2.6 mm to 1.4 mm (2.6-1.4 mm waveguide), respectively. The large bore of GTMW at the proximal end improves coupling efficiency, and the small side at the distal end enhances flexibility and concentration of energy. Three CBMW samples were fabricated, whose bore sizes are 1.4 mm (1.4-1.4 mm waveguide), 1.6 mm (1.6-1.6 mm waveguide), and 2.6 mm (2.6-2.6 mm waveguide), respectively. Polycarbonate (PC) capillary is chosen as the substrate tube for flexibility. The PC capillary is manufactured by glass-draw technique [29]. By changing the drawing speed, the gradually tapered tube is achieved. The silver (Ag) film is inner-plated through a liquid-phase chemistry process [30,31]. Figure 1(b) is the picture of the 2.6-1.6 mm waveguide sample. It can be seen that bore size of the waveguide gradually decreases. The five waveguide samples are of the same length of 1 m.
Fig. 1. (a) Structures of GTMW and CBMWs with same sizes of large bore and small bore as GTMW. (b) Picture of manufactured 2.6-1.6 mm waveguide.
2.3 System
Figure 2 shows the experimental system for 0.3 THz wave transmission and imaging. 0.3 THz wave emitted from terahertz source (Terasence, IMPATT-300) [32]. The wave is coupled into a coupler by a TPX lens with a focal length of 32 mm. The coupler is a 10 cm long CBMW with the same bore size as the measured waveguide. And the measured waveguide is directly coupled with the coupler. It should be noted that the coupler exists only when the bending loss was measured, as shown in Fig. 3. In the experiments of penetrability measurement and imaging, the coupler was removed and the terahertz wave was directly coupled into the sample waveguide after passing through the lens. The output signal is recorded by the terahertz pyroelectric detector (Gentec, THz-9B-BL). Imaging object was placed between the output end of the waveguide and the detector at a distance of 1 mm. The object was moving in two dimensions perpendicular to the light path during imaging. The scanning step length is 0.5 mm.
3. Experimental results and discussion
3.1 Transmission characteristics
Bending loss varying with curvature was measured for the five waveguide samples. Bending loss is calculated by the measuring data of the output power from the coupler (P2 in Fig. 2) and the waveguide (P3 in Fig. 2). In the measurements, 15 cm long input end and 20 cm long output end of the waveguide were kept straight. The remaining 65 cm long waveguide was uniformly bent with various bending radius. The source power was coupled into GTMW from larger bore side. Coupling loss can be ignored in the measurement, because the coupler and the measured waveguide are of the same bore size.
Figure 3 shows the measued bending loss of the five waveguide samples. Table 1 is the summary of typical measured losses. The theoretical loss of TE11 mode, dominant mode in metal hollow waveguide, is added for comparison. It can be seen that all waveguide samples follow the general 1/R bending loss dependence where the slope of the linear best fit denotes the sensitivity of the attenuation to applied bending. This is because bending excites high order modes and causes additional loss. We also conclude from Fig. 3 that waveguide with bigger bore size has a lower transmission loss. And the loss of GTMW is between that of CBMWs with the same bore size of input and output ends of the GTMW. In addition, the loss of 2.6-1.4 mm waveguide is larger than that of 2.6-1.6 mm waveguide. It is consistent with the theoretical analysis that the loss of GTMW increases with the increase of taper.
Table 1. Theoretical and measured losses for the waveguide samples
Furthermore, GTMWs exhibit a lower bending loss sensibility than that of their small constant bore counterparts. This can be explained by comparing the theoretical losses of TE11 mode and measured straight losses of waveguides in Table 1. It can be concluded that most of the energy is in TE11 mode in GTMWs. However, measured straight losses of 1.4-1.4 and 1.6-1.6 mm waveguides are far larger than theoretical losses of TE11 mode. It means that a large proportion of energy is in high-ordered modes, such as TM21 and TM11 modes, resulting in high bend loss.
3.2 Penetrability of output beam
The penetration ability (penetrability) of terahertz wave is of special importance in security screening. Three commonly used materials of container, paper, plastic, and ceramic, were selected to investigate the penetration capability of 0.3 THz wave output from each waveguide. The penetration rate is defined as the ratio of the output power passing through the materials. Figure 4 shows the penetration rate of 0.3 THz wave when using the five waveguide samples as the probes. The penetrability of the wave using GTMW probe is larger than that of their small constant bore counterparts. In addition, the penetrability of 2.6-1.6 mm waveguide is greater than that of 2.6-2.6 mm waveguide. The above results may be due to the higher energy concentration of the GTMW at the port. It means high photon density leads to high penetrability [33]. High penetrability is beneficial for imaging applications.
3.3 Imaging
Imaging is investigated by using the experimental system shown in Fig. 2. Scanning step length is 0.5 mm in the experiment. A shaving blade hidden between two papers was imaged by using the 2.6-1.6 mm waveguide as the imaging scan probe. The probe was bent to the angle of 180 degrees with the bending radius of 20 cm. Figure 5(a) is the picture of the blade with a length of about 4 cm and a width of about 2 cm. An oval like a hole with a long axis of 5 mm and a minor axis of 2 mm is in the middle of it. Scanning terahertz image is shown in Fig. 5(b). The shape of the blade, the hole at the center of the blade, and two holes at both sides of the blade are clearly seen. Signal intensities along the horizontal and vertical lines are shown in the left side and bottom side of the image in Fig. 5(b). Intensity increases obviously in the area of the holes. It is possible to guide the THz wave and realize imaging by using the flexible probe in a very limited space.
Fig. 5. Blade picture (a) and 0.3 terahertz imaging of blade using 2.6-1.6 mm waveguide as probe (b).
3.3.1 Imaging under straight configuration
Imaging performances were investigated with the waveguide probes in straight transmission. Two metal rods with a gap of 2 mm in parallel were imaging by using GTMW and CBMW samples. The waveguides maintain the straight configuration.
Terahertz image is shown in Fig. 6(a), the gap of 2 mm between the two metal rods can be clearly distinguished. Figure 6(b) shows the distribution of signal intensity. It is normalized with the maximum signal value at the middle of the two rods.
Fig. 6. (a) THz image of two metal rods with a gap of 2 mm in parallel imaged by 2.6-1.6 mm waveguide. (b) Normalized intensities derived from the cross-section of the topography data along horizontal line in the Fig. 7(a).
In order to quantify the imaging quality, an imaging error E is defined as follows. Large imaging error E means low imaging quality. As can be seen in Fig. 6(b), peak width when the normalized intensity dropped to 0.8 is set as a reference value. The E is defined as the percentage of difference between the peak width and the gap width.
It can be found in Fig. 6(b) that the imaging error of 2.6-2.6 mm waveguide is the largest and the imaging errors of 2.6-1.6 mm and 1.6-1.6 mm waveguides are relatively small.
It is a challenge to identify small gaps. The 2.6-1.4 mm waveguide sample was used as the imaging probe. Two parallel metal rods with 1 mm gap was the imaging object. The object was placed at 1 mm and 3 mm away from the output end of the waveguide. Figure 7(a) shows that the 1 mm gap could not distinguished when the distance was 3 mm. This is because the output beam has a large divergence angle for the probe. Nevertheless, the 1 mm gap was clearly identified when the distance was 1 mm. It means that the distance of 1 mm is close enough to distinguish the gap.
Fig. 7. (a) Normalized intensities with waveguide end - object distance of 1 mm and 3 mm. Imaging qualities under straight configuration. (b) Normalized intensities of 2.6-2.6, 2.6-1.4 and 1.4-1.4 mm waveguides, (c) Intensities of 2.6-2.6, 2.6-1.4 and 1.4-1.4 mm waveguides, (d) Normalized intensities of 2.6-2.6, 2.6-1.6 and 1.6-1.6 mm waveguides, (e) Intensities of 2.6-2.6, 2.6-1.6 and 1.6-1.6 mm waveguides.
Imaging quality to the 1 mm gap between two rods was investigated by using the fabricated five waveguide samples. In all the following experimental configurations, the probe is 1 mm away from the sample. Measured signal intensity and normalized intensity are shown in Figs. 7(b)–7(e). It can be concluded from the Figs. 7(b) and 7(d) that the imaging qualities of the GTMW probes are lower than their small constant bore counterparts. Because the GTMW is of larger output divergence angle than that of the CBMW [20], resulting in a larger output beam and a decrease of imaging quality.
In addition, the E of 2.6-1.6 mm waveguide is close to that of 2.6-2.6 mm waveguide due to the combination of large divergence angle and small output bore size. Similarly, Figs. 7(b) and 7(d) show that the imaging quality of 2.6-1.4 mm waveguide is lower than that of 2.6-1.6 mm waveguide. Because the divergence angle of GTMW output beam increases with the slope of the taper [20]. It can also conclude from the Figs. 7(c) and 7(e) that 2.6-1.6 mm waveguide shows sharper peak than that of the 2.6-1.4 mm waveguide.
The imaging quality of each waveguide is compared from another point of view. Table 2 shows output power of five waveguides for direct coupling. In this measurement, the 0.3 THz wave was coupled into the waveguide samples without the coupler. The source power is 8.5 mW obtained at the focus of the lens (P1 in Fig. 2), and directly coupled into GTMW delivering from big bore end to small bore end. It can be concluded that although the large divergence angle of GTMW output beam reduces the imaging quality, it has high coupling efficiencies with source. And low transmission loss allows more energy to be delivered. Figures 7(c) and 7(e) further demonstrate the conclusion, showing that peak energies of GTMW output beams in the gap are several times stronger than that of small constant bore waveguides. Moreover, the peak energy of 2.6-1.6 mm waveguide is only 24% lower than that of 2.6-2.6 mm waveguide. This means high penetrability for GTMWs and thus lower requirements for detector performance.
Table 2. Output power of waveguide samples for direct coupling
3.3.2 Imaging under bent configuration
It is also important to maintain the imaging quality when waveguides are bent. The imaging qualities of GTMW and CBMW probes under bent configuration were also experimentally studied. All results were obtained when the waveguides were bent 180 degrees with the bending radius of 20 cm. Figure 8 shows the comparisons of normalized intensities obtained by 2.6-1.4 (a), 2.6-1.6 (b), 2.6-2.6 (c), and 1.6-1.6 (d) mm waveguides under straight and bent conditions. It can be seen that imaging quality by GTMW is barely reduced after being bent. However, bent CBMW greatly reduces the imaging quality. These results can be attributed to that bending results in mode mixing and high order mode generation in constant bore waveguides [13,19,34], generally resulting in scattering output beam and low imaging quality. Nevertheless, small output bore of GTMW enhanced concentration of energy, which resists the influence of bending. We note that imaging performance of 1.4-1.4 mm waveguide is not included because the output power of bending is too weak to obtain reliable results.
Fig. 8. Influence of waveguide bending on imaging. The comparison of imaging qualities of 2.6-1.4 (a), 2.6-1.6 (b), 2.6-2.6 (c) and 1.6-1.6 (d) mm waveguides under bending and straight configurations.
4. Conclusion
In summary, in this research, the transmission and imaging capabilities of gradually tapered metal hollow waveguide (GTMW) and constant bore metal waveguide (CBMW) at 0.3 THz are investigated. The waveguide losses change with the structure parameters is well predicted by theoretical calculation. The GTMW is flexible, easy to be fabricated and relatively insensitive to bending. Its output wave has larger penetration ability. Especially, more than 4 times as much energy as small bore CBMW is delivered by GTMW under same source configuration due to low loss and high coupling efficiency. The influence of bending on the imaging quality of GTMW is much less than that of CBMW. The advantages of GTMW are of great significances in the transmission and robust imaging system. It suggests that further refinements in the waveguide structure will allow for improved imaging and transmission capabilities.
Funding
National Defense Science and Technology Innovation Special Zone; Natural Science Foundation of Shanghai (19ZR1405000); National Natural Science Foundation of China (61775060, 61975034).
Disclosures
The authors declare no conflicts of interest.
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