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Abstract
Terahertz band is envisaged to provide substantially higher capacity and much lower latency for wireless communications in contrast to microwave frequencies. Moving to higher frequencies comes with its own unique challenges to be addressed, such as poor coupling efficiency from free space into and out of planar air-core waveguides. Here, we propose a framework for rapid design and low-cost fabrication of terahertz horn couplers. The horn couplers are first designed by maximizing the field overlap integral on apex and aperture interfaces, then fabricated exploiting 3D printing technique, and finally sputtered with a thin layer of gold. A 28~μm standard deviation of the surface roughness height of the 3D printed horn couplers is calculated. Experimental demonstrations show that the proposed horn coupler improves the transmittance of a hybrid photonic crystal waveguide by 20 dB in comparison with the previous pinhole-based coupling configuration. This work provides a fast, convenient and economical approach for design and fabrication of customized couplers for any waveguide size, with a cost of only 5% of commercially available counterparts, and could be integrated in 3D-printed terahertz devices during fabrication.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the development of technology, our society is becoming more and more dependent on information interchange. The total global mobile network data traffic has doubled in just two years since 2020 [1]. The peak data transmission rate is expected to reach $10$ Gbps in current 5G era, and continue increasing to $1$ Tbps in the coming 6G era [2]. The terahertz (THz) band ($0.1-10$ THz) shows potential to fulfill the future demands for 6G wireless systems. THz communication has strengths such as up to hundred GHz bandwidth, pico-second-level symbol duration, integration of thousands of sub-millimeter-long antennas, and weak interference without full legacy regulation [3].
Waveguides play an important role in any integrated THz system, improving free-space path, stability, portability and footprint. Various THz waveguides [4–9] and fibers [10–15] have been studied to identify the best to meet the need. Of particular interest are waveguides with sub-wavelength cores (improving footprint), and air (hollow)-core waveguides, due to the unsurpassed transparency of dry air at THz frequencies [16,17]. However, efficient signal coupling from free space into such sub-wavelength cores and vice versa is a challenge: conventional lenses commonly used in THz systems, and in particular THz time-domain spectroscopy systems [5,12,18,19] cannot match the narrow input mode profile. For instance, we have recently demonstrated a hybrid photonic crystal (HPC) waveguide working at $0.37-0.41$ THz with a sub-wavelength scale air-core, where the propagating wave is confined in the lateral and vertical directions by silicon pillars and parallel gold-coated plates, respectively [4] - but the coupling efficiency was only $11\%$ from a free-space Gaussian beam.
A solution to improve the coupling efficiency is through the use of horn couplers, which transforms a large mode into a narrow mode, as long as the tapering of the cross section is adiabatic [20,21]. While horn couplers have been studied for radio and microwaves since the late $19^{\rm th}$ century [22], metallic horn couplers are now also available commercially at the low end of the Thz spectrum, for coupling into and out of metallic waveguides. Commercially available horns are designed for waveguide sizes defined by Electronic Industries Alliance (EIA) [23,24]. The couplers for EIA waveguide dimensions cover broad frequency ranges, from sub-GHz to hundreds of GHz, but only cover discrete sets of waveguide sizes - which do not match more experimental waveguides so that they result in limited coupling improvement for the latter. Moreover, commercial horn couplers are commonly fabricated using conventional machining methods, which given the small sizes especially at higher frequencies are not readily available to most laboratories on short timescales [25].
The emergence of 3D printers and additive technology has enabled cost-effective and fast fabricating cycle of arbitrary and complex 3D structures [26–28], including horn antennas and couplers for microwave and millimeter-wave frequencies [29–34]. The continuing improvement of the resolution of 3D printers (down to a few microns) has led to harnessing the technology for fabrication of THz devices including waveguides and fibers [5,35,36], antennas [37,38], lenses [39–41], and couplers [42–44]. To date, 3D-printed horn couplers for EIA waveguide sizes have mainly been demonstrated for D-band ($110-170$ GHz) [43], and H-band ($220-325$ GHz) [43,44]. Thus, nowadays with the tremendous research focusing on development of THz communication devices, having a cost-effective solution for rapid design and fabrication of THz bespoke couplers with high coupling efficiency becomes a necessity.
In this work, a solution for rapid design and low-cost fabrication of bespoke horn couplers is proposed. Using this method, we design, fabricate and experimentally demonstrate a THz horn coupler with enhanced coupling efficiency from free space into and out of a HPC waveguide. The dimensions of the output and input end of the horn are calculated by maximizing the field overlap integral, and the length is determined based on the adiabaticity criterion. The optimized horn structure provides $84.5\%$ coupling efficiency from a free-space Gaussian radiation into the tightly confined HPC waveguide in the frequency range of $0.37-0.41$ THz. Experimental measurements show improvement of around $20$ dB for the transmittance of the HPC waveguide in comparison with the previous pinhole-based coupling configuration, which also significantly reduces the power loss due to better coupling, as a result making the devices more environmentally friendly. In addition, the cost of 3D-printed horn couplers is only $5\%$ of commercial metallic horn couplers. To the best of our knowledge, this is the first demonstration of design and fabrication of a 3D-printed horn coupler in Y-band frequency range ($325-500$ GHz).
2. Design, fabrication and experimental verification
In this section, we explain the technical detail of our approach for rapid and cost-effective design and fabrication of a bespoke horn coupler as well as the experimental detail. While the design steps are general and applicable for enhancing coupling efficiency into/out of most waveguides. Here, we implement the proposed solution to enhance coupling efficiency from free space into/out of a specific HPC waveguide [4].
The HPC waveguide, demonstrated in Ref. [4], is consist of silicon pillars sandwiched between parallel plates, where vertical and lateral confinement is achieved due to reflection from metallic plates and photonic bandgap gap, respectively. The HPC waveguide, in Ref. [4], have large bandwidth (around $70$ GHz with the centre of the bandgap at $0.39$ THz), lower losses and dispersion compared to their single material counterparts, making it an a promising platform for future integrated THz communication devices. In this work, we use the same HPC waveguide samples as Ref. [4] with two lengths including $42$ mm and $72$ mm. Each waveguide has two channels with different numbers of rows of pillars in the cladding ($10$ rows and $15$ rows hereafter called channel 1 and 2, respectively). The width and height of the air core is $485~\mu$m and $300~\mu$m, respectively, in all HPC waveguide samples. In Ref. [4], a pinhole with diameter of $1.2$ mm was used at the focal point of a lens to couple THz radiation into the HPC waveguide samples and block the stray beams.
Here, in section 2.1, we discuss the design process of the horn coupler by calculating the optimal dimension of the apex, aperture and length. In section 2.2, we describe the fabrication process and THz experimental setup.
2.1 Coupler design
The first step is to find the ideal dimension for the apex ($a$ and $b$ in Fig. 1), and the aperture ($a'$ and $b'$ in Fig. 1) of the horn coupler, such that it leads to the maximum coupling efficiency from free space to the air-core waveguide, here a HPC waveguide.
Fig. 1. Schematic of the horn coupler structure, where $a$ and $b$ are the width and height of the apex side, respectively; $a'$ and $b'$ are those of the aperture side. $L$ is the length of the horn coupler.
The coupling efficiency between the fields at the interface of two devices (where one can be free-space) is given by the overlap field distribution integral (overlap integral in short) of the fields $\eta$ of the modes on either side of the interface [45,46]. Our first step is thus to optimize $\eta$, first at the apex and then at the aperture. The overlap integral can be calculated using the following equation:
As the fundamental mode at the apex of the horn coupler is the same as that of a rectangular waveguide with the same dimension of the apex, we find the horn apex dimensions so that the transverse field overlap integral between the fundamental mode of the HPC waveguide (obtained from numerical simulation) and $TE_{10}$ mode of a rectangular waveguide is maximized. In this case, we perform a parameter sweep to find the width of the apex ($a$) only, as the height ($b$) is defined by the height of the air-core HPC waveguide, which is $300~\mu$m. The transverse field overlap integral indicates that a $519~\mu$m $\times ~300~\mu$m waveguide cross section will lead to $97.16\%$ coupling efficiency at $0.39$ THz (center of the bandgap), as shown in Fig. 2(a). Then, we calculate the overlap of $TE_{10}$ mode between a rectangular waveguide and a Gaussian beam to maximize coupling efficiency from free space. The spot size of the Gaussian beam for our THz system at $0.39$ THz is $800~\mu$m (measured using knife edge measurement [47]). The transverse field overlap integral indicates that a maximum $88\%$ coupling efficiency can be achieved, as shown in Fig. 2(b). The efficiency is reduced slightly to $87\%$ after making the adjustment so that the horn coupler is physically realizable (maintain same aspect ratio as the apex side). This step defines the horn aperture size: $2.137$ mm $\times ~1.233$ mm ($a'$ and $b'$ in Fig. 1, respectively). Therefore, the maximized total coupling efficiency (from free-space Gaussian beam to the horn, followed by the HPC waveguide) could be up to $84.5\%$.
Fig. 2. Field overlap integral between (a) a rectangular waveguide and the fundamental mode of a HPC waveguide; (b) a rectangular waveguide and a Gaussian beam. (c) and (d): Normalized transverse electric field simulations of coupling from free space in and out of the HPC waveguide, respectively (top view).
Finally, to find the proper length, we calculate the required adiabaticity criterion of the length of the horn based on the equation $L\geq \frac {a'^{2}}{2\lambda }$, where $\lambda$ is the wavelength [48], giving a minimum length of $3.3$ mm. We choose $5$ mm and $10$ mm as the length of the coupler, which is longer than the adiabaticity criterion. The simulated field of coupling THz waves from free space in and out of the HPC waveguide are shown in Fig. 2(c) and (d), respectively, which clearly show the process that the THz waves are collected from free space into the HPC waveguide by the horn coupler, and then emitted from the output side with only moderate back reflections.
Table 1 summarizes the design and performance parameters of the proposed 3D-printed horn coupler, compared with coupling between a free-space Gaussian beam, as well as standard commercial horn couplers from two different manufacturers with operating frequency covering that of the HPC waveguide ($370-410$ GHz). The operating frequencies of commercial horn couplers are based on EIA waveguide sizes, which are listed in the table. The operating frequency range of the rectangular ports is defined as $1.25f_{c}-0.95f'_{c}$, where $f_{c}$ and $f'_{c}$ are the cutoff frequencies of the fundamental mode and the second-order mode, respectively [49]. In Table 1, the total coupling efficiency to the HPC waveguide of the commercial horn couplers is calculated using the same method as the 3D-printed coupler explained above. Results show that the coupling efficiency of both WR2.8 and WR2.2 commercial horn couplers are higher than the free-space Gaussian beam, but still more than $3.5$ times lower than the 3D-printed ones. This is because the apex and aperture size of the commercial horn couplers are designed for EIA waveguide sizes, which is not suitable for efficient coupling into the HPC waveguide. This is while, our proposed horn coupler can reach a high coupling efficiency - more than three times higher than the WR2.2 commercial horn couplers and more than seven times higher than the free-space Gaussian beam.
Table 1. Comparison of dimension, operating frequency range, and coupling efficiency of the 3D-printed customized horn coupler, commercial horn couplers, and a free-space Gaussian beam.
2.2 Fabrication and experiment
We use an Asiga Max UV 3D printer ($62~\mu$m horizontal and $10~\mu$m vertical resolution [50]) and polymer resin printing material (Asiga DentaMODEL) to fabricate the horn couplers. This material has good adhesion to gold and has minimum deformation after gold sputtering. The light intensity of the 3D printer is $23.8$ mW/cm$^{2}$; and the slice thickness is $0.01$ mm. In order to make the inner surface of the horn coupler fully covered by gold during the sputtering process, we print the samples in halves as shown in Fig. 3(a). After 3D printing process, a $250$ nm gold layer is sputtered on the inner surface of the horn couplers, which is thicker than the skin depth of the gold ($118-124$ nm) at the working frequency range of the HPC waveguide ($0.37-0.41$ THz). The gold layer adhered completely to the 3D-printed material, shown in Fig. 3(b). More details of the gold sputtering process can be found in Ref. [5]. Finally, the two halves of the horn couplers are assembled together (see Fig. 3(c)).
Fig. 3. Photographs of $5$ mm and $10$ mm 3D-printed horn couplers without assembling (a) before and (b) after gold sputtering. (c) Gold sputtered horn couplers after assembling.
We use a fiber-coupled compact time-domain THz spectrometer, TeraSmart from Menlo Systems for measurements, with up to $4.5$ THz spectral range and $80$ dB dynamic range. The schematic of experimental system (THz radiation part) is shown in Fig. 4. The incident signal from the transmitter (Tx) is almost a symmetrical Gaussian beam and focused by two polymer plano-convex lenses with $50$ mm effective focal length. The output signal from the samples is then focused into the receiver (Rx) by another pair of polymer plano-convex lens. We have conducted two sets of experiment, one to measure the transmittance through HPC waveguides using horn couplers (see Fig. 4(a)) and the other one to measure the transmittance through only horn couplers (see Fig. 4(b)). The measurements are all normalized transmittance, where the measured power is normalized to that of a reference signal: the reference signal for the HPC waveguide is the transmittance through only two horn couplers in the system without the HPC waveguides (see Fig. 4(b)), and the reference signal for horn couplers is the transmittance when there is no sample in the system and the lenses are positioned confocally. Note that to reduce the alignment error when only horn couplers are characterized, we have printed the two horn couplers in one piece (attached to each other on the apex side, see the inset in Fig. 5).
Fig. 4. Schematic of the experimental setup for characterization: (a) the HPC waveguide and (b) the horn couplers. Tx is the transmitter and Rx is the receiver. The inset is a photograph of the horn coupler assembled on a metal plate, which is used to block the stray beams and hold the horn couplers.
Fig. 5. (a) Measured transmittance of a $42$ mm HPC waveguide with (solid curves) and without (dash curves [4]) two $10$ mm horn couplers for channel 1 (blue curves) and 2 (green curves). The error bars indicate the standard deviation of the measurements. Area with shadow is the $3$ dB bandwidth. (b) Measured transmittance of double horn couplers in different length (black curves for $10$ mm and green curves for $5$ mm) without waveguide, and a pinhole with diameter similar to the horn apex (blue curve). The inset is a photograph of the one-piece double horn couplers.
3. Results and discussion
The measured transmittance of a $42$ mm HPC waveguide with two $10$ mm horn couplers and through a $1.2$ mm-diameter pinhole at the input side is shown in Fig. 5(a). The measurements are repeated $10$ times to minimize the alignment errors; and the results in the figure is the average with standard deviation indicated by the error bars. Note that in Ref. [4] the reference signal for the HPC waveguide through a $1.2$ mm-diameter pinhole at the input side is the transmittance through only the pinhole in the system without the HPC waveguides. For channel 1 (ch1), the transmittance is improved around $17$ dB compared to that of a $1.2$ mm-diameter pinhole used in Ref. [4]. For channel 2 (ch2), the improvement of transmittance is around $20$ dB. The $6$ dB and $8.5$ dB loss in the transmittance is due to the waveguide loss ($0.03$ dB/mm [4]), and the manual alignment between horn couplers and the waveguide. Since misalignment can happen in $x, y$ and $z$ directions, we conducted numerical simulations to study the effect of the horn shifting along the three axes on both sides at the same time. We observed that a $20~\mu$m misalignment along $x$ axis does not introduce much loss, while similar misalignment along $y$ and $z$ axis can lead to around $5$ dB and $10$ dB loss in the bandgap frequency range ($0.37-0.41$ THz), respectively (see Fig. S2 in Supplement 1). This can explain the loss observed in the measurements shown in Fig. 5(a). The $3$ dB bandwidth (shadow area) of channel 1 and 2 are $69$ GHz and $61$ GHz, respectively. For comparison, we conduct the measurements for the HPC waveguides using two $5$ mm-long horn couplers. Results show that the coupling performance to the waveguides of $10$ mm horns are around $2$ dB better than the $5$ mm ones, which we attribute that to having longer adiabatic lengths (i.e. lower reflection losses or higher antenna gain, see Supplement 1 Fig. S4). Similar results are also observed in $72$ mm HPC waveguide (see Supplement 1 Fig. S1).
We have also measured the transmittance via double horn couplers (both $5$ mm and $10$ mm long) without the waveguide to test their performance, shown in Fig. 5(b). The transmittance of a $500~\mu$m diameter pinhole, which is close to the width of the horn apex ($519~\mu$m), are also measured for comparison purposes. The double-horn samples are printed in one piece to avoid loss from alignment between two horns (see inset in Fig. 5(b)). Experimental measurements show that both samples have improved transmittance in the operating range of the HPC waveguide ($0.37-0.41$ THz) compared to the $500~\mu$m diameter pinhole. The $5$ mm horn coupler has higher transmittance due to less propagation and surface roughness loss. We attribute the $10$ dB loss of the horn couplers to manual alignment of the system and surface roughness from 3D printing.
To investigate the surface roughness from 3D printing, we conduct reflection measurements of polished (using $800$-grit sand paper) and non-polished 3D-printed block samples sputtered with the same thickness gold as the horns. The experimental setup for reflection measurements is shown in Fig. S3(a) in Supplement 1. A $0.9$ dB loss per reflection is observed at $0.37-0.41$ THz (the operating frequency range of the HPC waveguide) for normal incidence (see Fig. S3(b) in Supplement 1). We calculate the standard deviation of the surface roughness height of the non-polished 3D-printed block sample based on the method demonstrated in Ref. [51]. The standard deviation is $28~\mu$m, which is similar to the resolution of the 3D printer. The loss may increase when the incident wave has an angle and accumulate when the THz waves propagate inside the horn coupler as there are multiple reflections, which may lead to the total $10$ dB loss observed in Fig. 5(b). Similar surface roughness is observed in a 3D-printed straight air-core rectangular waveguide, which has a loss of $1.5-2$ dB/mm at frequency range of $75-110$ GHz [52]. Surface roughness from 3D printing could be reduced by either physical polishing or chemical methods [53,54].
4. Conclusions and outlook
We propose a solution for rapid design and low-cost fabrication of bespoke THz horn couplers. Using this method, we design, fabricate and demonstrate a 3D-printed THz horn coupler with only $5\%$ cost of commercial ones, improving the transmittance of a HPC waveguide by $20$ dB in comparison with the previous pinhole-based coupling configuration. The $10$ mm-long horn couplers have higher coupling performance through the HPC waveguide compared to that of $5$ mm-long horn couplers due to longer adiabatic lengths. This is while, the loss of $10$ mm-long horn couplers are higher due to longer propagation length and the surface roughness. This work provides a fast, convenient and economical way of customized couplers for any waveguide size and can be applied for THz chip integrations in THz wireless communication systems.
Funding
Fundamental Research Funds for the Central Universities (2022JBZY004); National Natural Science Foundation of China (62075007).
Acknowledgments
S.A. acknowledges UNSW Scientia program. This work was performed in part at the UNSW Node of the Australian National Fabrication Facility (ANFF).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
Supplemental document
See Supplement 1 for supporting content.
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