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Abstract
Nascent data-intensive emerging technologies are mandating low-loss, short-range interconnects, whereas existing interconnects suffer from high losses and low aggregate data throughput owing to a lack of efficient interfaces. Here, we report an efficient 22-Gbit/s terahertz fiber link using a tapered silicon interface that serves as a coupler between the dielectric waveguide and hollow core fiber. We investigated the fundamental optical properties of hollow-core fibers by considering fibers with 0.7-mm and 1-mm core diameters. We achieved a coupling efficiency of ∼ 60% with a 3-dB bandwidth of 150 GHz in the 0.3-THz band over a 10 cm fiber.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The emergence of extremely data-intensive technologies such as Web3, applied artificial intelligence (AI), and immersive realities are bound to drive and power future applications [1]. As one can expect, this would lead to an exponential increase in both data creation and consumption coupled with a corresponding rise in demand for faster, uninterrupted transmissions [2]. The fifth-generation wireless communication technology is already falling short in supporting the early development of these technologies owing to bandwidth limitations that throttle the highest achievable data rates [3]. Researchers have explored several solutions that include multilevel multiplexing techniques to bypass bandwidth limitations toward achieving higher data rates [4]. However, these solutions involve highly complex design inputs, are difficult to manufacture and require a much larger footprint. With possibilities of terabit-per-second (Tbit/s) connectivity, the terahertz- (THz) and sub-THz-band frequencies will be the center of the sixth generation (6 G) communication network and beyond [5]. Indeed, the THz frequency range from 100 GHz to 10 THz represents a huge unexploited spectral range that can be leveraged to realize high-data-rate communication links without any additional spectral enhancement techniques [4]. According to the Shannon theorem, the bandwidth generally increases at higher frequencies leading to a rise in channel capacities [6]. The THz range has enormous potential and has supported the development of applications for improved imaging towards super-resolutions [7], ranging [8], and wireless communications [9].
In addition, efficient low-loss THz interconnects have been reported and could be prime candidates for meeting the ever-growing demand for higher data rates in short-range interconnection applications. THz interconnects can help bridge the gap between the existing interconnections and the insufficient capabilities of inter- as well as intra-chip interconnections. The much-needed short-range interconnects are in the range of a few centimeters and are designated as “the last-centimeter interconnect" [10]. All-silicon (Si) dielectric THz waveguides have already demonstrated applications towards 6 G and beyond, with extremely low loss of < 0.1 dB/cm and ∼ 350 GHz bandwidth [7]. Noteworthy dielectric waveguides include photonic crystal waveguides, effective medium (EM) waveguides, and unclad dielectric wire waveguides. Even though photonic crystal waveguides have reported a low loss of < 0.1 dB/cm, they possess a limited bandwidth of approximately 20 GHz [11,12]. EM waveguides are just as low-loss as photonic crystal waveguides, but reportedly possess a higher bandwidth of 120 GHz at the 0.3 THz band and 350 GHz at the 1 THz band [7,13]. However, the design of EM waveguides is complex and requires high-precision machining. Further, the unclad waveguides reported a low loss (< 0.1 dB/cm) and bandwidth similar to that of EM waveguides [7,14]. Despite the attractiveness of dielectric waveguides, they do not intrinsically offer the flexibility needed for chip-to-chip and board-to-board interconnections because they are made of high-resistivity (10 kΩ-cm) crystalline Si. Lately, hollow-core fibers have gained considerable attention as efficient, flexible interconnects [15,16]. Hollow-core fibers coupled with Si photonic crystal waveguides have reported a loss of 2 dB/m with a bandwidth of 50 GHz and 10 Gbit/s data rates over a 1-m expanded polytetrafluoroethylene (ePTFE) fiber [17]. However, the coupling efficiency between the Si waveguide and the fiber was limited to ∼ 30%. More recent studies have reported a PTFE core fiber link with 20 Gbit/s data rates under on-off keying (OOK) modulation over 25 cm [18]. When the fiber link employed a three-dimensional (3D)-printed coupler the fiber loss was 20 dB/m, which resulted in a coupling loss as high as 10 dB. In both studies, the fiber core with cladding was directly exposed to air, resulting in poor robustness of the fibers.
In this work, we propose a THz fiber link by leveraging the low-loss feature of dielectric waveguides and the flexibility of hollow core fibers to achieve a higher coupling efficiency between the fiber and Si waveguide. The hollow core fiber made of silica glass with a silver coating allows for greater robustness while maintaining its flexibility [19]. We investigated the coupling between the Si waveguide and silver-coated fiber by examining the fundamental optical properties of the hollow core fibers.
2. Design
2.1 Modal analysis of terahertz fiber
The hollow core fiber is made of a silica glass tube with an inner silver coating, as reported in reference [19]. The thickness of the inner silver coatings was around 200 nm, which is larger than the skin depth for the THz wave. For the inner diameter of the fiber, we considered two cases with 0.7- and 1-mm core diameters. Modal analysis of the hollow core fiber can be performed by assuming a circular cross-sectional hollow waveguide. We investigated the dispersion bandwidth of the THz fiber. For high-capacity communication, it is not only important to have a broad transmission bandwidth of the waveguides, but also a broad dispersion bandwidth to avoid signal distortion due to group delay dispersion [20]. The dispersion curves for each type of fiber were calculated using COMSOL Multiphysics and are presented in Fig. 1 (a) and 1 (b) for the 1-mm core and 0.7-mm core fibers, respectively. Fig. 1(a) and 2 (b) confirm the five modes supported by the 1-mm core fiber and two modes supported by the 0.7-mm core fiber. The corresponding mode profiles for the 1-mm core fibers of TE11, TM01, and TE21 are shown in Fig. 2(a), 2 (b), and 2 (c), respectively. For the 10-cm long fiber mode (blue), the dispersion bandwidth of the 1-mm core fiber (Fig. 3(a)) is 28 GHz at the center frequency of the WR2.8 band (260–390 GHz), i.e., 330 GHz, and the 3-dB bandwidth for 0.7-mm core fiber (Fig. 3(b)) is ∼ 13 GHz. Thus, the 1-mm core fiber can realize approximately twice the high-capacity communications rate compared to that of the 0.7-mm core fiber. Because the propagation constant β of a circular hollow waveguide is expressed by a hyperbolic function [25], as the frequency increases relative to the cutoff frequency the dispersion becomes linear which results in lower signal distortion owing to differences in group velocity. Consequently, a 1-mm diameter fiber with a lower cutoff frequency for the fundamental TE11 mode is less susceptible to the effects of group delay, and hence, a better candidate for high-capacity communication applications.
Fig. 1. Dispersion curves of (a) 1-mm core, (b) 0.7-mm core fibers showing the propagation constant as a function of frequency. Blue, red, green, purple, and black lines denote TE11, TM01, TE21, TM11, and TE01 modes, respectively.
Fig. 2. Mode profiles of 1mm-core fiber: (a) TE11, (b) TM01, and (c) TE21. Color map shows the electric-field intensity of in-plane component.
Fig. 3. Dispersion bandwidth as a function of frequency: (a) and (b) for 1-mm, and 0.7-mm core, respectively. Blue, red, green, and purple lines denote 10, 30, 60, and 100 cm length, respectively.
The results of the modal analysis were confirmed by theoretical calculations of the cutoff frequency fc for each mode supported by the fibers using Eq. (1) [21]:
where $P_{\textrm{nm}}^{\prime}$ represents the zeros of Bessel functions of the first kind [19], c is the velocity of light in free space, r is the radius of the circular waveguide, ε is the permittivity constant, and µ is the permeability constant. Based on Eq. (1), the cutoff frequency fc of each mode for the 0.7-mm and 1-mm core fibers is summarized in Table 1.
Table 1. Cutoff frequencies for various modes
As can be seen in Table 1, the number of guided modes in the fiber increases with diameter. That is, the fiber of 0.7-mm diameter supports fewer modes than the fiber of 1 mm diameter. For the fiber of 0.7-mm diameter, only the fundamental TE11 mode and the TM01 modes are supported for operation in the WR2.8 band, which covers frequencies from 260 to 400 GHz. For the other modes, fc is beyond the frequency range of interest. For the 1-mm diameter fiber, five modes have fc within the frequency range of interest. These calculations confirm our initial modal analysis.
2.2 Design of silicon waveguide interface
Figure 4 details the realization of the fiber link based on a Si wire waveguide interface. An unclad Si waveguide is chosen as an interface for the fiber link because these waveguides are low-loss and broadband in comparison to photonic crystal waveguides. Unclad waveguides reported bandwidth of ∼120 GHz and up to 350 GHz at higher frequencies [14]. The unclad waveguide is built upon an EM waveguide by removing a portion of the EM section. The EM section serves to implement all-Si frames that are used in the experiments for handling as well as protection of the unclad waveguide core.The EM section was realized by introducing an array of through-holes in a 200 µm thick Si slab with refractive index of 3.418, and resistivity > 10 kΩ·cm. Introducing an array of holes into the Si slab makes it possible to engineer a material with a refractive index between that of intrinsic silicon and that of air.
Fig. 5. Simulated wave impedance and reflection coefficient. (a) Simulated wave impedance of the effective-medium-clad waveguide (red) and the fiber (blue). (b) Simulated reflection coefficient at the waveguide-fiber interface.
The resulting material has a refractive index that is strongly dependent of a and d, where a represents the lattice constant and d the hole diameter. Values of a = 150 µm, d = 117 µm, and w = 336 µm in the proposed design were obtained after a careful parameter sweep for the optimal wave confinement of the waveguide.
Good impedance matching between the Si taper and the fiber is crucial for better coupling performance. The simulated wave impedances of the silicon effective-medium-clad waveguide and the fiber are shown in Fig. 5(a), where the impedance of the hollow fiber is close to that of the free space and has a relatively large difference from that of the Si waveguide. To this end, an Si tapered structure is introduced to allow the propagation mode in the waveguide to be gradually coupled into the hollow fiber with enhanced impedance matching. Consequently, as illustrated in Fig. 5(b), the simulated reflection coefficient at the waveguide-fiber interface is well below -20 dB. Such a low level of reflected THz energy is not expected to impact the link efficiency. The unclad waveguide is terminated by a linear taper on either end to serve as a coupler for both the fiber and hollow metallic waveguide which is necessary to interface with the measurement equipment. Among various taper shapes, linear tapers have been proven to allow gradual transmission of THz waves with < 0.2 dB loss [22]. The length of the taper has been chosen as 3 mm to optimize coupling efficiency. The analysis of the impact of the taper length on the coupling efficiency is shown in Fig. 6. Figure 6 shows that the coupling increases with the length of the taper. Therefore, a 4 mm taper can achieve a coupling as high as ∼90%. However, as the length increases, the taper is more susceptible to breakage. As a result, the length of the taper was chosen to be 3 mm for better coupling and robustness.
Fig. 6. Coupling efficiency of various taper lengths. Green, blue, red, and black denote 4 mm, 3 mm, 2 mm, and 1 mm, respectively.
The design of the waveguide coupler interface is critical for achieving good modal matching between the fundamental mode TE11 of the fiber and the Ex mode of the unclad wire waveguide. The unclad waveguide supports fundamental mode Ex as shown in Fig. 7.
Considering the mode profiles presented in Fig. 2(a-c), the Si wire waveguide mode Ex (Fig. 7) could only be coupled efficiently to the fundamental TE11 fiber mode in Fig. 2(a). As a result, although the 1-mm core fiber supports five modes, the designed waveguide interface only allows for the unclad wire waveguide Ex mode to be coupled to the fundamental TE11 mode of the fiber, thereby achieving quasi-single mode operation of the fiber.
The performance of a 1-cm long unclad waveguide alone was evaluated in a simulation employing CST Studio to confirm the minimal loss of the unclad waveguide alone, close to the ideal value of 0 dB across 260–380 GHz. Thereafter, the transmittance of each mode of the fiber to the unclad waveguide was analyzed using the same software. The coupling between the unclad waveguide and the fiber was performed through a linear taper that was 3 mm long and fully inserted into the fiber. The results are presented in Fig. 8(a) and Fig. 8(b) for 1-mm core, and 0.7-mm core, respectively. For the fundamental-mode TE11, the transmittance is very close to the ideal value of 0 dB for both the 1-mm core and 0.7-mm cores. The transmittance of TM01 was -20 dB approximately, which is indicative of the negligible coupling of this mode to the unclad waveguide. This is attributable to the fact that only the Ex mode of the Si wire was excited in this simulation. The value of -20 dB indicates the TM01 mode is not strongly coupled to the Si wire waveguides. This has been demonstrated through the modal analysis and confirmed by theoretical calculations as well. This is not the case for the remaining modes, i.e., TE21, TE01, and TM11, which are non-existent in the 0.7-mm core fiber. For the 1-mm core fiber, these modes have a transmittance of < -100 dB. This confirms that even when a fiber of 1 mm diameter supports multiple modes, only the fundamental mode TE11 is strongly coupled to the unclad waveguide, thus allowing pseudo-single-mode operation.
Fig. 8. Fiber mode coupling to unclad waveguide: (a) 1 mm core fiber, (b) 0.7 mm core fiber. Blue, red, green, purple, and black lines denote TE11, TM01, TE21, TM11, and TE01 modes, respectively.
3. Experiment
3.1 Loss measurement
To estimate fiber loss, we probed the power transmission in fibers of different lengths using the experimental setup shown in Fig. 9(a). Two sets of fibers with 1-mm and 0.7-mm core diameters were prepared, and four fibers with lengths of 10, 30, 60, and 100 cm were tested for each set. A signal generator was employed to generate a millimeter-wave signal that was inputted into a 9-times multiplier coupled to a WR-2.8 band hollow waveguide that delivers a THz range signal into the fiber through the unclad wire waveguide interface. A variable attenuator was attached to the hollow waveguide to maintain a constant safe power level in the mixer. The waveguide acted as a coupling interface. On the detection side, a THz range mixer was employed to perform frequency down-conversion, for producing microwave signals that were processed using a spectrum analyzer. Positioning jigs were employed to position the waveguides, for ensuring vertical alignment without tilts. This helps reduce imperfect alignment between the hollow metallic waveguides and the unclad waveguide as well as between the unclad waveguide and the fiber. A photograph of the experimental setup is shown in Fig. 9(b).
Fig. 9. Experimental setup for the measurement of the transmittance of fibers: (a) block diagram, (b) photograph of the setup, (c) Measured transmittance of 1 mm core fiber, (d) measured transmittance of 0.7 mm core fiber. Blue, red, green, and purple denote 10 cm, 30 cm, 60 cm, and 100 cm fiber lengths.
The measured transmittances of the 1-mm and 0.7-mm core fiber are presented in Fig. 9(c) and Fig. 9(d), respectively. The 1-mm core fiber achieved better transmittance than the 0.7-mm one. The difference in performance increased as the fiber length increased. An average transmittance of approximately - 5 dB for the 10-cm fiber was achieved by both the 1-mm and 0.7-mm core fibers. Similar performances for the 1-mm and 0.7-mm cores were achieved for the 30-cm and 60-cm fibers, with average transmittances of approximately - 9 dB and - 11 dB, respectively. However, for the 1 m long fiber, the difference in performance is significant with a transmittance of - 15 dB for the 1-mm core fiber and - 20 dB for the 0.7-mm core fiber. The lower transmittance of the 0.7-mm core fiber can be ascribed to the dispersion phenomenon of this fiber, as discussed in the previous section.
Probing the transmission power of the four fibers with different lengths allows the estimation of propagation and coupling losses. The four measurements for 10, 30, 60, and 100 cm correspond to four data points that were fitted to a curve using the least squares method. Subsequently, the propagation and coupling losses can be deduced using the slope and intercept of the curve. In other words, the slope corresponds to the propagation loss and the intercept corresponds to the coupling loss. An illustration of this procedure for a 1-mm core fiber at 320 GHz is shown in Fig. 10(a). The results for a 10 cm-long fiber in the entire WR-2.8 band are presented in Fig. 10(b) for the 1-mm core fiber, and Fig. 10(c) for the 0.7-mm core fiber. It can be seen in Fig. 10(b) and Fig. 10(c) that the measured propagation losses (red) are ∼1 dB and 1.5 dB for the 1-mm and 0.7-mm core fiber, respectively. The simulated propagation loss is in good agreement with the measured propagation loss for both fibers with averages of ∼1 dB and ∼1.5 dB for the 1-mm and 0.7-mm core fibers, respectively. The measured coupling loss (blue) is ∼2 dB and ∼2.5 dB on average for the 1-mm and 0.7-mm core fiber, respectively. Although the average value of the simulated coupling loss is comparable in the case of the 1-mm fiber, it shows less variation. This could be ascribed to the difficulty in accurately inserting the Si linear taper inside the fiber in the experiments. This difficulty is reflected in the increased coupling loss of the 0.7-mm core fiber in comparison to the 1-mm core fiber, owing to the much smaller diameter of the 0.7-mm core fiber. These results show that the 1-mm core fiber has reduced losses and is more suitable for applications in THz-range communications, which require a higher power level.
Fig. 10. Estimated propagation loss (red) and coupling loss (blue) of fiber: (a) Curve-fitting and estimation for 1 mm core diameter fiber at 320 GHz, (b) 1 mm core diameter fiber, (c) 0.7 mm core diameter fiber. In (b) and (c), the coupling loss is given for 1 port, and the propagation loss is shown for 10 cm long fibers. Measured values are presented in solid lines and simulated values are in dashed lines.
Fig. 11. THz fiber link communication experiments: (a) Block diagram, (b) photograph of the experimental setup.
3.2 Communication experiments
Based on the measurements of the fibers, we employed both 1-mm and 0.7-mm core fibers for the realization of high-data-rate fiber links through communication demonstration. THz sources already suffer from limited power [23]. Taking into consideration additional losses from the individual components of the fiber link, a 1-mm core fiber with reduced loss is expected to exhibit better performance. Although multiple modes exist in the 1-mm core fiber, only the fundamental TE11 mode is excited through the developed Si waveguide interface, as described previously. Figure 11(a) and 11 (b) present the block diagram of the communication experiment and a photograph of the experimental setup, respectively. For demonstration, an arbitrary wave generator (AWG) delivered data that is used to modulate the optical signal from two laser sources using the OOK modulation scheme. The modulated signal was subsequently amplified by an erbium-doped fiber amplifier (EDFA) and down-converted by a uni-traveling-carrier photodiode (UTC-PD) to deliver a THz signal at 320 GHz. The resulting signal was then injected into the unclad waveguide through a metallic hollow waveguide. The unclad waveguide guided the THz waves into the THz fiber through the tapered coupling interface. During detection, a second unclad waveguide is used to interface with a metallic hollow waveguide, which was connected to a Schottky barrier photodiode (SBD). The transmitted data were extracted by the SBD through envelope-detection demodulation. A low-noise amplifier with a bandwidth of 18 GHz was employed to amplify the demodulated signal before it was reshaped using a limiting amplifier. The corresponding eye diagram and bit error rate (BER) were assessed using an oscilloscope and a bit error rate tester (BERT), respectively.
The results presented in Fig. 12 show the detected BER as a function of the transmitted data rates. For this measurement, an 80-mV bias voltage was applied to the SBD to enhance the sensitivity [24]. Practical error-free (BER of < 10−11) communication was achieved at data rate of up to 22 Gbit/s for the 1-mm core fiber, whereas at 24 Gbit/s data rate the BER increased to 2 × 10−3. For the 0.7-mm core fiber, the maximum error-free data rate was 14 Gbit/s. This could be ascribed to the exacerbated dispersion phenomenon that further reduced the dispersion bandwidth of the fiber, which was much lower than the theoretical value of 13 GHz estimated in theory. The eye diagrams for data rates of 10 Gbit/s and 14 Gbit/s for 0.7-mm core fiber, and 18 Gbit/s and 20 Gbit/s for 1-mm core fiber are provided. It can be noticed that both fibers experience some level of amplitude distortion, which is reflected in a high eye-crossing percentage of >80%. Such distortion could be attributed to the failure of the measurement system to perform data pulse symmetry efficiently. Provided eye diagrams also suggest a low signal-to-noise ratio (SNR) for both fibers, resulting in limited data rates of 22 Gbit/s and 14 Gbit/s for 1mm-core and 0.7-mm core fibers, respectively.
Fig. 12. Performance of proposed THz fiber link for communication applications: recorded BER as a function of data rates for 0.7-mm core fiber (red) and 1-mm core fiber (blue) with associated eye diagrams for 22 Gbit/s (1-mm core fiber) and 14 Gbit/s (0.7-mm core fiber).
Subsequently, to demonstrate the robustness of the fiber for practical applications, we implemented the demonstration of high-definition (HD) video transmission over 1 m-long fiber. The experimental setup is similar to Fig. 11(a), except for the data source which in this case is a video player. In addition, we employed a different transmitter, i.e., F-band (90–140 GHz) UTC-PD, together with a W-band (75–110 GHz) amplifier and a multiplier to deliver THz signal at 300 GHz. This allowed us to get -6 dBm output power, enough for the transmission of the HD video. At the detection, a video display was employed after the SBD to show the received video. We achieved the transmission of the video as shown in Fig. 13. This demonstration showcases the robustness and flexibility of the THz fiber, but also introduces novel applications that were not demonstrated by previous work.
Fig. 13. Demonstration of THz non-line-of-sight wired communications, transmission of HD video (See Visualization 1).
The recorded performance of the fiber link is summarized in Table 2, together with previous work. Table 2 reveals that this fiber link has a competitive performance in terms of loss for short lengths up to ∼30 cm. In addition, the recorded coupling efficiency is the highest among all fibers. Although for longer lengths, this fiber has increased loss, a major advantage remains its robustness. This has made it possible to implement significant bend for the demonstration of HD video transmission.
Table 2. Comparison between reported hollow-core THz fiber links
4. Conclusion
We introduced a low-loss and high-data-rate THz fiber link using an efficient dielectric-waveguide interface. The proposed waveguide interface allowed the pseudo-single-mode operation of the fiber to achieve error-free data rates of 22 Gbit/s with OOK modulation. The fiber link demonstrated superior results compared to those of previous studies. The demonstrated fiber link holds the potential for chip-to-chip, board-to-board, and module-to-module THz interconnects.
Funding
Core Research for Evolutional Science and Technology (CREST) program of the Japan Science and Technology Agency (JPMJCR21C4); Japan Society for the Promotion of Science (KAKENHI), (20H00249); National Institute of Information and Communications Technology (NICT), Japan, commissioned research (03001).
Acknowledgments
We would like to sincerely thank Dr. Shuichi Murakami, Dr. Yoshiharu Yamada, and Dr. Yusuke Kondo for the fabrication of the Si waveguides.
Disclosures
The authors declare no conflict of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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