1. Introduction

The advance of terahertz (THz) science and technology provides cutting edge technique in broadband communication, biology imaging, medical diagnostic and home-land security surveying [1–4]. In order to take full advantage of THz waves, there is an urgent need for developing functional THz devices to control THz waves. THz waveguide is among the top lists. However, the community is still struggling to design and manufacture high performance devices working in THz band meeting the following criteria: low loss, easy fabrication and low cost.

A large number of waveguides are currently being explored, including metallic waveguides and dielectric waveguides. The non-planar metallic waveguides consisted of circular waveguides suffering from high metallic losses [5], parallel plate waveguides [6], bare metal wire structure [7], two-wire structure [8] and slit waveguide [9]. Most of them are only suitable for mm length scale due to a strong trade-off between mode confinement and metallic loss [10]. The dielectric waveguides for THz guidance have also already been reported, which can be divided into three class based on different guiding mechanism [11]: solid core [12, 13], porous core [14, 15] and hollow core waveguides [16–23]. Both solid-core and porous-core sub-wavelength fibers are sensitive to external perturbations and bending. Hollow-core waveguides, consisting of an air-core and a structured cladding, can alleviate external disturbances as most of the field is guided within the air core region [24]. Several designs based on hollow core structure have been proposed, such as photonic band gap type fibers [16, 17], Kagome type fibers [18–21], and dielectric tubes [22, 23]. As an example for metallic waveguides, a bare metal wire is reported that a 0.9 mm diameter stainless steel wire has an attenuation constant less than 0.03 cm⁻¹ and almost zero dispersion from 0.25 to 0.75 THz [7]. The fabricated plastic photonic crystal fiber with a high index core exhibits the low loss of 0.5 cm⁻¹ within the bandwidth of 0.1-3 THz [12]. A spider-web porous fiber has exhibited the loss less than 0.08 cm⁻¹ between 0.2 and 0.35 THz with the minimum of 0.003 cm⁻¹ at 0.24 THz [15]. A hollow core Bragg fiber with a cladding of triangular-lattice of air cylinders operating near 0.105 THz with low transmission loss 0.069 cm⁻¹ was demonstrated [16]. Lai et al. [22] have shown that a pipe waveguide has achieved an attenuation constant less than 0.02 cm⁻¹ and a 0.2 THz bandwidth. Kagome photonic crystal structure offers exceptional low loss, wide bandwidth and flexible control over the guided mode characteristics. The concept of Kagome fiber was previously demonstrated at infrared and optical frequencies [18, 19]. In the infrared region, a Kagome-lattice hollow core photonic crystal fiber offers optical attenuation with a baseline of 0.00041 cm⁻¹ (180 dB/km) over a transmission bandwidth larger than 200 THz [18]. And a similar fiber exhibits low transmission loss with 0.00016 cm⁻¹ (70 dB/km) at 600 nm, and 0.00030 cm⁻¹ (130 dB/km) at 532 nm in visible spectral range [19]. There are a few experimental works on fibers of Kagome photonic crystal structures guiding THz radiation [20, 21]. In 2008, a Kagome-lattice optical fiber guiding THz radiation is first proposed, which composed of a central hollow core and a cladding layer formed by periodic arrangements of Teflon tubes [20]. A low attenuation constant less than 0.01 cm⁻¹ between 0.2 and 0.8 THz has been achieved and the frequency of the high transmission bands could be adjusted by linear scaling the fiber size. Furthermore, the measured attenuation constant can be found to be as low as 0.002 cm⁻¹ at the 0.77 THz, which is more than two orders of magnitude lower than the bulk material. Then a Kagome hollow core photonic crystal fiber made of PMMA tubes was reported [21]. The average power attenuation constant is about 0.6 cm⁻¹ in the range of 0.65 to 1.0 THz, which is on average 20 times lower than the bulk material.

Another key challenge remaining to be overcome involves the practical difficulties in component fabrication. Several fabrication approaches, including photolithography or micromachining work flows [21, 23, 25], high-temperature and hazardous hot-draw processes [7, 26], hand assembly [27] and draw tower [28], have been reported. The draw tower method mainly consists of two stages: preform fabrication and fiber drawing [28]. For the complicated structure such as Kagome photonic crystal fiber, fabrication technique may include stacking of capillary tubes, drilling holes in the bulk material, casting into a micro-structured mold, extrusion, and so on. The precise reproduction of the designed structure requires great efforts to optimize the facility’s parameters. Fortunately, 3D printing is a process for manufacturing prototype parts directly from computer models, which enables almost infinite possibilities for rapid prototyping [29]. In this sense, 3D printing technology show some advantage in its simplicity and flexibility in the production of Kagome photonic crystal fiber. However, 3D printed Kagome type waveguide has been barely reported, although 3D printing method has recently been employed to realize other type THz waveguides [16, 30–33],

In this work, we investigate 3D printed THz waveguides based on Kagome photonic crystal structure, inspired by the low-loss wide bandwidth hollow-core terahertz inhibit coupling fibers designed in our previous work [34]. The micro-structured THz fiber may be much more attractive, since one could manipulate the characteristics by introducing well designed core and/or cladding structure [35, 36]. We investigate all-dielectric hollow core waveguides, which confine THz in air core with the cladding designed to prohibit from coupling outward. Several waveguides of identical cross-section and various lengths were fabricated, and the propagation properties of the waveguides are characterized by a THz time-domain spectroscopy (THz-TDS) setup. Besides, the evolutions of the loss of fundamental mode in THz waveguides are simulated by using commercial software COMSOL based on the finite element method (FEM). Experimental results agree well with simulation, exhibiting an average power loss of 0.02 cm⁻¹ (the minimum is about 0.002 cm⁻¹ at 0.75 THz). Although the structure of bare metal wire [7] and pipe waveguide [22] are remarkably simpler than Kagome type waveguide, in addition to the advantage of low loss, we could find that the bandwidth of Kagome type waveguide is broader. Because the guiding mechanism is based on total internal reflection, the solid core waveguide normally has broadest bandwidth among the above mentioned waveguide designs. For Kagome fiber waveguide, the transmission windows could also be adjusted by changing the strut thickness of cross section and the refractive index of material [34]. However, it worth noting that like the pipe waveguide [22], Kagome type waveguide may be multimode due to the large core diameters. Besides, since the length of THz waveguide created 3D printing may be limited by the performance of different printers, such as 15 cm [16] and 10 cm [32] in the previous works, we could obtain a longer one (more than the maximum tolerated length 30 cm) by connecting separate waveguides without any additional alignment, while maintaining the excellent performance.

2. 3D fabrication of THz waveguide

Figure 1(a) shows the cross section of our waveguide design. The diameter of the hollow is about 9 mm, and it is surrounded by the air holes with diameters of 3 mm and struct thickness of 0.35 mm as indicated in the insets of Fig. 1(a). The prototypes were fabricated using a commercially available 3D printer (Objet30 prime, Inc.). The substrate material is VeroWhitePlus polymer. The printer has a resolution of 600 dpi along x- and y-axes and 900 dpi along z-axis. It is worth mentioning that the maximum length is restricted by the working distance of the 3D printer. The cross section of fabricated waveguide is sketched in Fig. 1(b). Figure 1(c) presents the image of the obtained waveguides with three different lengths, i.e. 10 cm, 20 cm and 30 cm.

 

Fig. 1 THz waveguide design and fabrication. (a) Cross section of the ideal waveguide design. (b) Photograph of cross sectional view of a fabricated THz waveguide. θ indicates offset angle between two waveguides. (c) Photograph of full view of three waveguides with length of 10 cm, 20 cm and 30 cm, respectively. (d) Photograph of concatenated waveguide.

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Note that 30 cm is the maximum tolerated length of our 3D printer. Then, how to produce a longer waveguide? The solution could be extremely simple: connecting two waveguides mechanically. A mechanical splice means a permanent connection between two optical fibers without thermal welded joint as in a fusion splice, which can be constructed relatively quickly without the need for expensive specialized equipment such as a fusion splicer [37]. Figure 1(d) demonstrates such a mechanical splice by directly connecting two sections of waveguide with different lengths, i.e. 10 cm and 20 cm by a tube (also 3D printed) whose inner diameter fits the outer diameter of the waveguide, without any additional alignment.

3. Results and discussion

All the experimental investigations of the waveguide performance were carried out on a home-made THz time domain spectroscopy (TDS) system [38, 39]. Through fast-Fourier-transformation (FFT) of the measured THz waveform, both the phase φ and signal intensity I as a function of the frequencies can be resolved. In this work, 10 cm and 30 cm long waveguides are considered as the reference and sample, respectively. By comparing the phase delay Δφ and the signal intensity reduction with the reference, one will be able to quantify the refractive index n_sam and the attenuation coefficient α of the sample. The effective refractive index is calculated as:

The attenuation coefficient of the sample can be calculated [40]:

Following the procedures, the refractive index and the loss of the waveguide are outlined in Figs. 2(a) and 2(b). It could be observed in Fig. 2(a), the effective refractive index of the 3D printer fabricated waveguide varied from 0.99 at 0.2 THz to 0.999 at 1.0 THz. One dip around 0.35 THz could be noticed, which is associated with a high loss band appeared around 0.35 THz as shown in Fig. 2(b) depicting the transmission loss of the waveguide arise from the avoided crossings between the core mode and modes supported by the cladding [21]. Three transmission windows centered at 0.25 THz, 0.51 THz and 0.75 THz, could be clearly resolved in Fig. 2(b). The minimum loss reaches 0.010 cm⁻¹, 0.008 cm⁻¹ and 0.002 cm⁻¹, respectively. It is worth mentioning that the typical losses of the bulked VeroWhitePlus polymer sample are 2.080 cm⁻¹, 5.754 cm⁻¹ and 10.114 cm⁻¹ at these three frequencies, respectively. These values are even several orders of magnitude higher than the measured losses at so called low transmission bands indicated in Fig. 2(b). For example, the maximum experimentally obtained loss in Fig. 2(b) is about 0.080 cm⁻¹ (0.35 THz) and the second maximum at 0.61 THz equals 0.025 cm⁻¹. In fact, the locations of the transmission windows could be well predicted by the antiresonant reflecting optical waveguide (ARROW) model. The locations of registered high loss regions could be qualitatively explained by an antiresonant reflecting optical waveguide (ARROW) model which predicts the high loss frequencies as [41]:

 

Fig. 2 THz waveguide characteristics. (a) Measured and simulated effective refractive index of waveguides. (b) Loss coefficients for 30 cm waveguide (using transmission through 10 cm waveguide as reference). Black line, experiment data when humidity was about 35%. Blue line, experiment data when humidity was about 10%. Red line, simulation. Green lines, high loss frequencies.

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Besides, propagation performance of the designed waveguide has been verified by numerical simulations by using commercial software COMSOL [34]. The retrieved refractive indices and losses as functions of frequency are outlined as red lines in Figs. 2(a) and 2(b). The numerical simulation results agree well with the experimental observations indicating well controllable performance of the 3D printed THz waveguide. Note that the above mentioned studies are performed in dry air. When taking into account the water absorption in air, the experimentally measured transmission loss of the THz waveguide is indicated as the black line in Fig. 2(b) (humidity 35%). Though the transmission losses become higher, the lowest loss at 0.48 THz is still as low as 0.009 cm⁻¹.

Figure 3(a) compares the experimentally measured losses of the 30 cm long waveguide (black line) and the concatenated one having the same length (red line). In general, two waveguides have similar performance except that the high loss bands around 0.6 THz of the concatenated waveguide are slightly shifted and wider. Furthermore, attempt has been made to radially rotate one waveguide with respect to another. θ in Fig. 1(b) represents the rotation angle between two waveguides. The transmission losses of the concatenated waveguides are displayed in Fig. 3(b) for θ = 20°and 40°, respectively. In Fig. 3(b), three curves are quite close except that the losses are slightly higher if θ ≠ 0. It could be associated with the imperfect superposition of the core boundaries of two waveguides. In order to bypass this problem, one may choose hexagons design of the waveguide' outer shaper instead of circles.

 

Fig. 3 Spliced waveguide characteristics. (a) Loss coefficients of a single waveguide and a spliced waveguide with the same length. (b) Loss coefficients of a spliced waveguide with aligned, 20° and 40° misaligned core boundaries.

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4. Conclusion

The transmission characteristics of the 3D printed Kagome photonic crystal waveguide are well predicted by the corresponding numerical simulation. Experimental results agree well with simulation, exhibiting an average power loss of 0.02 cm⁻¹ for 0.2-1.0 THz (the minimum is about 0.002 cm⁻¹ at 0.75 THz), and different waveguides could be mechanically spliced to generate a long terahertz cable without any additional alignment, while maintaining the excellent performance. Besides the propagation loss, the 3D printed Kagome type waveguide in this work has advantages in the bandwidth and flexibility of the fabrication method. Except for the solid core fiber, the bandwidth of Kagome type waveguide is broader than other type reported waveguides [7, 16, 22], and which could be further adjusted by changing the strut thickness of cross section and the refractive index of material [34]. 3D printing technology could greatly simplify the fabrication of THz device without sacrificing the performance. Moreover, 3D printing provides a lot of freedom for rapid prototyping, which is very convenient, accurate, mass-production and flexible.