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Abstract
Implementing terahertz circuits and system designs relies on integrating reconfigurable devices such as switches, to fulfill a critical role in controlling and manipulating the flow of terahertz signals on the chip. Although there have been several demonstrations of on–off switching in the terahertz range, there have been no demonstrations of 1-to-$N$ switching, to our knowledge. This pronounced lack of dynamically reconfigurable routing has severely limited the achievable complexity of terahertz systems. To address this, we propose 1-to-$N$ switches made of cascaded disk resonators integrated into a substrateless silicon waveguide platform. A single switch can be controlled via photoexcitation using a low-power 658-nm laser focused onto the disk resonator, turning off the resonance and inhibiting coupling into a crossing port. The measurement results demonstrate that the proposed switch has low insertion loss, which can be attributed to the inherently low dissipation of the platform. The proposed on–off switch achieves a maximum insertion loss of 1.2 dB, and the maximum extinction ratio of the switch is 16.1 dB with 1.5 GHz of bandwidth. Furthermore, a 1-to-3 switch is monolithically integrated together with a Luneburg lens in order to project each of its output ports to a different far-field direction and, thereby, translate the switching operation into a form of reconfigurable beam control for future applications.
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1. INTRODUCTION
An all-silicon substrateless dielectric waveguide platform based on an effective medium has shown great promise for realizing diverse active and passive components into terahertz-integrated systems, owing to its ability to support broadband operation with high efficiency [1]. This platform is composed solely of high-resistivity silicon, where a solid waveguide core is surrounded by an in-plane effective medium cladding made of a subwavelength hole array. The platform has been shown to achieve extremely low attenuation, with the $E_{11}^x$ guided mode demonstrating an average loss of 0.075 dB/cm over the frequency range of 220 to 330 GHz [2]. This platform can accommodate various passive components including filters [3], 2D horn antennas [4], waveguide crossings [5], or frequency- and polarization-division multiplexers [6,7]. However, until now no reconfigurable devices, such as switches, have been demonstrated on this platform. Such devices are crucial for many functions, such as wave routing, phase shifting, and beam steering.
In recent years, extensive research has been conducted on terahertz variable attenuators, also known as on–off switches [8–13], that are operated via photoexcitation [8–12] and short-circuiting [13]. Various terahertz variable attenuators have been proposed based on photonic crystal cavities [8], topological photonic waveguides [9–11], and hybrid graphene plasmonic waveguides [12]. Some of these attenuators and switches rely on changing the properties of a material through photoexcitation, enabling the control of terahertz wave propagation. These devices only suppress the transmission of terahertz waves and do not facilitate directional switching [8–13]. There has been one example of a 1-to-2 switch in the literature, using a T-junction power splitting switch implemented into a parallel-plate waveguide. These switches are operated by electrically actuated liquid metal components to switch between the two output arms of the power splitter [14]. However, a parallel-plate waveguide is also an intrinsically multi-mode structure as it supports infinitely many in-plane propagating modes, which is a pronounced disadvantage from the perspective of signal integrity.
In this paper, we introduce terahertz 1-to-$N$ switches that utilize integrated disk resonators on a substrateless silicon waveguide platform. The switches operate through photoexcitation with visible light, allowing the resonance to be turned off. Previously, we presented the design and simulation of a single on–off switch based upon photoexcitation [15], and here we incorporate an additional waveguide coupler that enables guided waves to be routed to one of the two output ports. The performance of this platform relies on the balance between system losses and the evanescent coupling of light with an access waveguide, to achieve what is known as critical coupling [16]. An advantage of this scheme is that multiple on–off switches can be cascaded to realize 1-to-$N$ switches, and we demonstrate this principle with a 1-to-3 switch. The photo-selective routing of the proposed switch is experimentally verified. Finally, one possible application of this terahertz switch is demonstrated, where a 1-to-3 switch is monolithically integrated together with an effective-medium-based gradient-index Luneburg lens to achieve beam switching.
2. DESIGN AND PRINCIPLE OF OPERATION
As shown in Figs. 1(a)–1(c), the proposed integrated terahertz on–off switch can be monolithically defined on a substrateless waveguide platform with a disk resonator in combination with two coupling waveguides. The output ports include the “bar” port or Port 2 and the “cross” port or Port 3, and this switch is designed to operate in the $E_{11}^x$ mode with in-plane polarization. The platform is made solely of high-resistivity silicon with a relative permittivity ${\epsilon _{{\rm Si}}}$ of 11.68 and a loss tangent of $3 \times {10^{- 5}}$ [17]. The effective medium cladding is defined by periodically perforating the silicon slab with cylindrical air holes in a hexagonal lattice configuration, as shown in Fig. 1(c), with the perforation period much smaller than the shortest guided wavelength ${\lambda _{{\rm g,h}}}$ over the operating frequency range. Waveguiding is enabled through total internal reflection, which is facilitated by the contrast in the relative permittivities between the solid core and the cladding. The homogenized relative permittivity of the effective medium can be obtained according to the Maxwell–Garnett effective medium theory [18,19], yielding ${\epsilon _x}$, ${\epsilon _y}$, and ${\epsilon _z}$ of 2.75, 3.84, and 2.75, respectively.
Fig. 1. Terahertz on–off switch using an integrated disk resonator on substrateless dielectric waveguide platform. The waveguides with a width, ${w_{0}}$, of 225 µm are built into a free-standing wafer with a thickness of 250 µm. (a) Top view; the unperforated silicon slab is for handling purposes, while the taper structures are for mode transition between the sample and the feeding hollow waveguides in measurements. The dimensions of the terahertz on–off switch are 10 mm in width and length. (b) Coupling region of disk resonator with a radius, $r$, of 863 µm and a separation from the waveguide, ${g_{1}}$ and ${g_{2}}$, of 20 µm. The red dot is a pumping area of the red laser. (c) Hexagonal lattice of the effective medium cladding with perforation period $a$ of 100 µm and an air hole diameter $d$ of 90 µm. (d), (e) Simulated instantaneous field distributions are plotted in linear scale at 275 GHz for the neutral and pumped switch resonator, respectively.
The proposed switch operates by photoexcitation that utilizes the optical fluence from a red laser to control the conductivity of the disk at the top surface and the edge far from the waveguides as shown in Fig. 1(b). The location is selected to avoid interfering with the terahertz waves propagating along the waveguides. The structure functions as an on–off switch by using photoexcitation above the bandgap energy of silicon at 1.12 eV, i.e., a wavelength shorter than 1107 nm, to turn on and off the resonance for terahertz waves. The switch operates in two states. In the neutral state, with the laser off, waves from Port 1 couple into the disk resonator, resonate, and couple out via the second waveguide to Port 3. In the pumped state, with the laser on, optical excitation results in excessive free carriers in silicon, leading to enhanced conductivity that affects the cavity resonance and inhibits terahertz resonance coupling to the disk [15]. Consequently, the terahertz wave from Port 1 is transmitted to output Port 2, while the resonant coupling to Port 3 through the disk is suppressed. To further visualize this concept, the simulated instantaneous field distributions presented in Figs. 1(d) and 1(e) indicate that the wave transmission channel can be controlled by optical excitation. The operation bandwidth is obviously limited by the bandwidth of the resonator, to be demonstrated in Section 3.
In order to investigate the principle of operation of the switch, it is necessary to model the photoexcitation of carriers at the edge of the disk resonator. During optical excitation, when photons with energies greater than the bandgap of the silicon are absorbed, the electron–hole pairs are generated, yielding a higher conductivity, i.e., higher absorption of terahertz waves, and damping the $Q$-factor of the resonance. To model the influence of the optical excitation, we initially calculate the optical fluence $F$ to determine the carrier concentration ${N_{\rm e}}$ in the pumped silicon as follows [20]:
where $R$ is the power reflection coefficient at the air–silicon interface, $P$ is the power spectrum density of the red laser, $A$ is the pumped silicon area, $h$ is Planck’s constant, $c$ is the speed of light in vacuum, and ${\lambda _{{\rm laser}}}$ is the wavelength of the red laser. Next, the plasma frequency ${\omega _{\rm p}}$, and collision frequency $\gamma$ are determined by the carrier concentration ${N_{\rm e}}$ and the carrier mobility ${\mu _{\rm e}}$, which is related to concentration via an empirical model [21], as follows [22]: where ${\epsilon _{0}}$ is the vacuum permittivity, $e = 1.602 \times {10^{- 19}} \;{\rm C}$ is the elementary charge, ${\epsilon _{0}} = 8.854 \times {10^{- 12}} \;{\rm F/m}$ is the vacuum permittivity, and ${m_{{\rm eff}}} = 0.26{m_{0}}$ is the carrier effective mass, with ${m_{0}} = 9.109 \times {10^{- 31}} \;{\rm kg}$ denoting the electron mass. Now the real part of the conductivity ${\sigma _{\rm r}}(\omega)$ can be derived as [23]Fig. 2. Simulated transmission and reflection profiles of the on–off switch in two states, i.e., neutral and pumped states. (a) Reflection coefficients. (b) Transmission between Port 1 and Port 2. (c) Transmission between Port 1 and Port 3. Drude parameters for the photoexcited silicon are ${\omega _{\rm p}} = 2\pi (1.6 \times {10^{14}})\;{\rm rad}/{\rm s}$ and $\gamma = 2\pi (8.0 \times {10^{12}})\; 1/{\rm s}$ [15].
Fig. 3. Optical excitation measurement setup and simulated instantaneous field distributions of the 1-to-3 switch for the three-channel device. (a) Optical lenses 1 and 2 have focal lengths of 25.4 and 30.0 mm, for Disk 1 resonator and Disk 2 resonator, respectively. The two fiber collimators have focal lengths of 18.24 mm with a wavelength of 633 nm, and the two red lasers with a center wavelength of 658 nm. (b) Fabricated sample with the pumped region for the 1-to-3 switch. (c) Both disks light off. (d) Disk 1 light on, Disk 2 light off. (e) Both disks light on.
To validate the switch concept, an on–off switch is simulated using CST Microwave Studio, and the results are shown in Figs. 2(a)–2(c). In Fig. 2 in the neutral state, the transmission from Port 1 to Ports 2 and 3 is ${-}12.3\;{\rm dB} $ at 275 GHz and ${-}1.2\;{\rm dB} $, respectively. This result shows a 3-dB bandwidth terahertz transmission of 1.5 GHz. In contrast, by applying optical excitation onto the disk resonator, the resonance is turned off and the wave is transmitted to Port 2. The normalized transmission coefficient at Port 2 is ${-}0.9\;{\rm dB} $, and ${-}17.3\;{\rm dB} $ at Port 3, as shown in Figs. 2(b) and 2(c). The extinction ratios between the on–off state at Port 2 and Port 3 are 11.4 and 16.1 dB, respectively. In both switching states, the reflection coefficient is around ${-}16.0\;{\rm dB} $ at 275 GHz, as shown in Fig. 2(a), which indicates that the switch does not cause high reflection. The insertion losses in the systems are caused by coupling loss and radiation loss from the disk resonator. The coupling loss is due to the limited coupling region imposed by the fabrication process, while the radiation loss is caused by the curvature of the disk. Therefore, Figs. 2(b) and 2(c) show the inhibition of the resonance with optical pump power, which confirms that the $Q$-factor of the disk resonator is affected by the associated photo-induced high conductivity in the silicon [24]. In addition, the bandwidth of the on–off switch is related to the $Q$-factor as follows:
where ${f_r}$ is the resonance frequency, and $\Delta {f_{{3\,{\rm dB}}}}$ is the 3-dB bandwidth transmission. A higher $Q$ factor corresponds to a narrower bandwidth, while a lower $Q$ factor results in a wider bandwidth. To achieve a wider bandwidth in this design, cascading disk resonators with the same resonance frequencies can increase the overall bandwidth [25]. However, it is important to note that each additional disk resonator introduces additional coupling and radiation losses, which in turn results in higher insertion loss.
Table 1. Normalized Transmission Coefficient of the 1-to-3 Switch at 276.1 GHz
Fig. 4. Simulated and measured transmission and reflection profiles of the 1-to-3 switch for the three-channel device. (a)–(c) Simulated and measured reflection coefficients of three operating states at Port 1. (d)–(l) Simulated and measured transmission coefficients of three operating states at Port 2, Port 3, and Port 4, respectively.
3. DEMONSTRATION OF TERAHERTZ SWITCHES
To experimentally validate the switch concept, a 1-to-3 switch design has been fabricated as shown in Fig. 3(b). The sample is made from a 4-inch intrinsic float-zone silicon wafer with a thickness of 250 µm and a resistivity of ${\gt}10 \;{\rm k}\Omega \,{\rm cm}$. The fabrication is based on a standard deep reactive ion etching (DRIE) process. The device has dimensions of $20.8 \times 12.5\;{{\rm mm}^2}$, with a minimum distance of approximately 5 mm between the output ports to accommodate the necessary bending radius and the coupling with a rectangular waveguide during measurement. Furthermore, to prevent crosstalk between the cascaded disk resonators, a minimum clearance between the disks of approximately 1 mm is required. For larger values of the output ports, the area would increase proportionally. The measurements of the 1-to-3 switch are conducted by using a Keysight vector network analyzer with VDI WR-3.4 extension modules spanning 220–330 GHz. To demonstrate the switch operation, the measurement system involves an optical train setup to illuminate the edge of the disk resonator. As described in the previous section, switching on the laser damps the resonance and thus the coupling into the coupled port. We utilize a red laser pigtail fiber diode module with a center wavelength of 658 nm to control the resonance of the disk, as red lasers are more readily accessible. At this wavelength, the absorption coefficient [26] and the penetration depth are $2.70 \times {10^3}\;{{\rm cm}^{- 1}}$ and 3.7 µm, respectively. The $1/{e^2}$ spot size measured by a Thorlabs LC100 line camera is 1.26 mm. The maximum pump power of the red laser is 40 mW, yielding an average optical fluence of $32000 \;{{\rm W/m}^2}$ in its main beam.
The operation of the 1-to-3 switch can be described by three operating states, as summarized in Table 1. In the neutral states, there is no optical excitation for both resonators. The waves from input Port 1 are coupled into Disk 1 on resonance and coupled out via the second waveguide to Port 4, as shown in the electric-field distribution in Fig. 3(c). In the pumped states, there are two settings that can be achieved using two optical excitations. In the first pumped state, Disk 1 is under optical excitation suppressing transmission from Port 1 to Port 4. As such the waves can be transmitted from Port 1 to Port 2 through Disk 2, as shown in Fig. 3(d). In the last state, both resonators are under optical excitation. This results in the waves from Port 1 being transmitted to Port 3 or “the middle port” because the resonances of the two disk resonators are turned off, as shown in Fig. 3(e). Thus, the resonance coupling to Ports 2 and 4 through the first and second disks is suppressed.
In general, the simulated and measured results presented in Fig. 4 agree well. Discrepancies between simulations and measurements can be attributed to several factors, including fabrication tolerances and misalignment. These tolerances can result in non-ideal coupling, as previously discussed in the results of the on–off switch. Discrepancies observed in $|{S_{{11}}}|$ are relatively large due to its weak power level. The working resonance frequency of the 1-to-3 switch differs from that of the on–off switch due to the fabrication tolerance of the disk resonator diameter, which mainly controls the resonance frequency. From the measured results in Figs. 4(a)–4(l), the normalized transmission coefficient of the 1-to-3 switch at 276.1 GHz is listed in Table 1. These results indicate that the energy is effectively coupled to one of the output ports.
Practically, the insertion loss in this system is not only caused by the coupling loss and radiation loss of the disk but also the losses from unavoidable leakage to pumped resonators and non-operating ports. In practical implementation, it is challenging to completely suppress the resonance coupling into the disk resonator under optical excitation. The disk resonators can effectively damp the resonance only after the coupling event. More specifically, the resonator can only exhibit its desired frequency-selective behavior after coupling thereto has already occurred, which is the origin of the unavoidable increase in insertion loss in the case of a pumped resonator. The leakage to non-operating ports occurs due to the non-ideal coupling of the disk resonator is caused by fabrication limitations and tolerances in the separation gap. These can be observed in Figs. 3(c)–3(e) and are verified by the measurement results, which demonstrate some remaining transmitted power at inactive ports as shown in Fig. 4. The switching speed of this 1-to-3 switch depends on the recombination time of photoexcited carriers in the silicon, typically around 1 ms, resulting in a switching speed of approximately 1 kHz [27]. It is for this reason that we term the device a “switch,” and not a “modulator,” which would require a far higher switching speed. After all, these experimental results verify the proposed 1-to-3 switch concept. Each resonator can operate individually, enabling independent control of each unit channel. However, it is worth noting that cascading multiple disk resonators leads to increased insertion loss.
4. MULTI-BEAM SWITCHING WITH INTEGRATED ANTENNA
Here, we demonstrate the integration of the 1-to-3 switch with an integrated Luneburg lens to realize discrete beam steering without mechanical actuation. The Luneburg lens is a gradient index (GRIN) structure that maps a point source at the circumference to a far-field direction diametrically opposed to the location of the source. This mapping functionality makes it uniquely suited to realizing angular beam-steering so long as the feed point can be adjusted. Previously, an all-silicon Luneburg lens was demonstrated with high gain and efficiency [28], but did not incorporate any switching mechanism, and so each far-field direction was accessed by a separate input port. Thus, while the multiple feeds were characterized, true beam steering was not demonstrated. Now, with the proposed switches we can perform an illustratory example of beam steering based on this principle.
A detailed procedure for the design of an all-silicon Luneburg lens is outlined in Ref. [28], but for completeness, we include a brief overview. To achieve the desired focal mapping, we employ a radially symmetrical modal index profile defined by the equation [28]
Fig. 5. Luneburg lens design. (a) Photograph of the fabricated single Luneburg lens for characterization. (b) Radially dependent hole diameter profile used to realize the all-silicon Luneburg lens. (c) Parametric design of the optimized feed structure. In this case ${l_i}$ is defined iteratively as ${l_i} = {l_{i - 1}} + 10$, where ${l_0} = 10 \;{\unicode{x00B5}{\rm m}}$, and the hole diameter is a linear function varying between 32.8 and 48 µm.
In Ref. [28], a tapered waveguided was used to feed the lens. However, this technique has limitations—notably, it is dispersive. More specifically, the taper reduces confinement, resulting in most of the power being distributed outside the core, occupying a wide area. Consequently, it becomes a poor approximation of a point source, and hence is unsuitable as feed for the Luneburg lens. In Ref. [29], this was addressed by introducing a compact gradient index feed based on a slot waveguide to feed a half-Maxwell Fisheye lens. This lens is also implemented with an effective medium, so its feeding structure can straightforwardly be adapted to the Luneburg lens. Here, we utilize this approach to feed the Luneburg lens. In Fig. 5(c), the parametric design of the feed is shown, comprising two components, first a linear widening of the waveguide core, and second, a transition to a slot based on a gradient index transition. This design is then optimized to minimize the magnitude of the reflection coefficient $|{S_{{11}}}|$ obtained with a full-wave simulation of the single port Luneburg lens. The final parameters are shown in Fig. 5(c).
Fig. 6. Characteristics of the Luneburg lens. (a) Simulated and measured reflection coefficients of the single feed Luneburg lens sample over the frequency range of interest. (b) Simulated and measured gain of the single feed Luneburg lens sample at 276.98 GHz.
Fig. 7. Multi-beam switching with the 1-to-3 switch. (a) Schematic illustration of the switched-beam antenna under optical excitation. (b) Photoexcitation measurement setup. Red laser pigtail fiber diode modules have a center wavelength of 658 nm with a maximum power of 40 mW. Optical lenses 1 and 2 have focal lengths of 25.4 and 18.24 mm, respectively. The customized packaging is for handling purposes and is not situated in proximity to electromagnetically relevant components. (c) Photograph of the fabricated switched-beam antenna for characterization. (d) Micrograph of the tapered feed. (e) Micrograph of the disk resonator with access and coupling waveguides.
To characterize this antenna, the Luneburg lens with a single optimized port, shown in Fig. 5(a), is used. The sample is packaged inside a 3D-printed polylactic acid (PLA) mount and attached to a rotating stage for radiation pattern measurement. The antenna package is coupled to the WR3.4 waveguide output. The reflection coefficient, shown in Fig. 6(a), indicates reasonable alignment with simulations, with return loss far in excess of 10 dB. Then, using a rotating stage, a radiation pattern measurement in the $E$-plane is conducted and shown in Fig. 6(b). Next, another fabricated sample contains the 1-to-3 switch, with the corresponding output ports of the switches connected to three feeds surrounding the circumference of the Luneburg lens, giving the possibility for three discrete beams, arbitrarily selected at 0°, 30°, and ${-}{60^ \circ}$ as shown in Fig. 7(a). In theory, this scheme could be extended to many more feeds, though admittedly the optical feeding network becomes increasingly unwieldy. The operation of the switched beam can be described as follows: when Disk 1 is not illuminated, the beam is steered to a 30° angle via Port 4. When Disk 1 is illuminated and Disk 2 is not, the beam is steered to a ${-}{60^ \circ}$ angle via port 2. Finally, when both Disks 1 and 2 are illuminated, the beam is steered to a 0° angle via Port 3.
Fig. 8. Simulated and measured radiation patterns of the three-port switched beam at 276.98 GHz. (a) Both disks are in the neutral state for 30° output. (b) Disk 1 pumped for ${-}{60^ \circ}$ output. (c) Both disks are pumped for 0° output. (d)–(f) Measured radiation patterns of the three-port switched beam according to (a), (b), and (c), respectively.
The switched-beam antenna is characterized by the experimental setup shown in Fig. 7(b). The radiation pattern measurements of the various switched-beam states are conducted, and the free-standing switched beam is held with customized packaging. The radiation emitted by the Luneburg lens antenna propagates over a free-space distance of 220 mm, i.e., in the Fraunhofer far-field region, whereupon it is received by a WR-3-coupled diagonal horn antenna. In order to measure radiation patterns, the above process is carried out repeatedly over an angular range extending from ${-}{75^ \circ}$ to 75° with 0.25° steps on an automated rotation stage. The results of this procedure for the switched beam with a three-port antenna are given in Fig. 8. The measured radiation patterns are shown at a working frequency of 276.98 GHz. As illustrated in Figs. 8(a)–8(f), the measured and simulated beam profiles for both disks in the neutral states show the expected 30° output Port 4, with a maximum gain of 15.8 dBi. In the case where Disk 1 is pumped, the beam is switched to a ${-}{60^ \circ}$ angle output Port 2 with a maximum gain of 16 dBi. Finally, pumping both disks allows to achieve a maximum gain of 14 dBi at 0° angle output Port 3. The results indicate that the radiation efficiency is primarily limited by the efficiency of the cascaded switches. In addition to the main beams, sidelobes are observed in Figs. 8(a) and 8(b), and are caused by energy leakages from the disk resonator due to imperfect coupling of the energy into the selected disk resonator. These results successfully illustrate the switching of the beam to the desired angles, which validates the functionality of the integrated switch with the Luneburg lens, thereby emphasizing its potential for facilitating a larger number of beams. Nonetheless, it is crucial to highlight that the use of multiple cascaded switches to achieve a larger number of beams leads to an unavoidable increase in insertion loss.
5. CONCLUSION
The concept of terahertz 1-to-$N$ switches employing disk resonators has been realized on a substrateless dielectric waveguide platform. The proposed switch can operate under photoexcitation of the disk resonators, which direct energy into different output ports. The proposed device can achieve low insertion loss due to the inherent low loss of the platform itself. The experimental results show that a 1-to-3 switch can achieve an average insertion loss of 2.62 dB with a bandwidth of 1.50 GHz, while the respective maximum extinction ratio can reach 13.82 dB. The 1-to-3 switch on this platform has been integrated with a Luneburg lens to realize beam switching. The experimental results demonstrate the designed switched-beam functionality in three directions. This underscores the switching capability of multi-beam switching compared to traditional resonant antennas. These proposed switches can be used as a building block to serve various terahertz applications such as wave routing, beam steering, and photonic switching for sensing, imaging, and communications. This contributes to a promising pathway for future terahertz-integrated systems.
Funding
Australian Research Council (DP220100489).
Acknowledgment
The authors acknowledge the facilities as well as the scientific and technical assistance of the Research and Prototype Foundry Core Research Facility at the University of Sydney, part of the NSW node of the NCRIS-enabled Australian National Fabrication Facility. We thank Gloria Qiu and Jacky He for assisting the device fabrication. Daniel Headland acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 801538.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this study are not publicly available at this time but may be obtained from the authors upon reasonable request.
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