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Abstract
Terahertz radiation as an upcoming carrier frequency for next-generation wireless communication systems has great potential to enable ultra-high-capacity transmissions with several tens of gigahertz bandwidths. Nevertheless, dispersion is one of the main impairments in achieving a higher bit rate. Here, we experimentally demonstrate a compact terahertz dispersion compensator based on subwavelength gratings. The gratings are fabricated from the low-loss cyclic olefin copolymer exploiting micro-machining fabrication techniques. With the strong index modulation introduced in the subwavelength grating, the high negative group velocity dispersion of -188 (-88) ps/mm/THz is achieved at 0.15 THz for x-polarization (y-polarization), i.e., 7.5 times increase compared to the state-of-the-art reported to date for terahertz. Such high negative dispersion is realized in a grating of 43 mm length. The asymmetric cross-section and periodic-structural modulation along propagation direction lead to considerable birefringence that maintains and filters two orthogonal polarization states, respectively. These polymer-based birefringent gratings can be integrated into terahertz communication systems for dispersion compensation of both long-haul wireless links and waveguide-based interconnect links.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the last few years, terahertz (THz) technology has evolved dramatically due to the successful implementation of interesting applications such as high-speed communication, non-destructive material inspection, biological sensing, security, and many others [1]. To accommodate the ever-increasing demand for mobile data [2], the THz band is considered as the carrier frequency that can offer ultra-high data rates for next-generation wireless communications (6G) [3]. The dispersion of THz waves is one of the limiting factors for THz communication links since high dispersions reduce the transmission data rates [4]. Although the dispersion of THz waves in the atmosphere is relatively low (typical group velocity dispersion (GVD) value of 2.5 × 10−5 ps/mm/THz at 0.15 THz [5]), it would become considerable when THz waves are transmitted through a dispersive interconnect (waveguide) or long-haul backup links for satellite assisted wireless communication [6]. To put it into perspective, an average time delay of a 100-km wireless THz link or a 2.5-m THz waveguide (GVD value of ∼1 ps/THz/mm) could be up to 375 ps at 0.15 THz. To this end, waveguide-based devices with high negative values of GVD become indispensable at the receiver end. In the well-known field of optical fiber communication systems, fiber Bragg gratings have been illustrated as an effective technique to mitigate the dispersion [7].
Although the gratings have been extensively applied in optics [8,9], the demonstrations at THz frequencies are still limited despite the great demand for important functionalities such as dispersion manipulation [5] and filtering [10,11]. The challenge stems from the implementation of gratings in the THz waveguides. Considering dry air is the most transparent medium for THz waves, promising waveguide platforms that mitigate high transmission losses of polymers are either subwavelength THz fibers (propagation mainly in the air cladding) [12–14] or air-core structures with exotic cladding designs (propagation in the air core) [15–18]. To date, only one study [5] based on hollow-core THz metallic waveguide Bragg grating was reported to compensate for positive dispersion in the THz communication links. A negative GVD of only -25 ps/THz/mm (at 0.14 THz with transmission losses of over ∼10 dB) was achieved in a 100-mm long grating. The reported grating had weak modulation, was polarization-independent, and suffered from multimode operation due to large core diameter.
Furthermore, manipulation of two polarization states is also important for polarization-sensitive THz systems, as it could double the channel capacity of THz communication links [19]. However, in the context of THz gratings filters, current demonstrations either filter one polarization state or are polarization independent. For instance, a THz notch-type Bragg grating written on a polymer fiber was reported for filtering applications nevertheless, the filtering of one polarized state was unnoticeable due to fabrication limitations — laser cutting technique caused the asymmetric distribution of etched gratings on circular rod [20]. Another THz waveguide grating has been demonstrated based on a plasmonic two-wire waveguide accompanied by paper grating, yet it only filters the wave perpendicular to the paper grating [21,22]. Furthermore, very recently, a THz all-silicon grating filter integrated on an effective-medium-clad waveguide was demonstrated which also filters only one polarization state [11].
To achieve large negative GVD along with effective polarization control, here, we realize THz subwavelength birefringent polymer fiber gratings fabricated using micromachining techniques. We experimentally demonstrate the negative GVD of -188 ps/mm/THz in a 43 mm device length, which is more than 7.5 times higher dispersion reported to date in THz waveguide-based gratings. In the context of dispersion compensation for both long-haul wireless link and short-range fiber interconnector (time delay of 375 ps at around 0.15 THz), the required length of subwavelength grating is more than halved in contrast to that of other gratings. Further, our experimental results confirm the filtering of two orthogonal modes (polarization-maintaining) at 0.15 THz.
2. Design and fabrication
Figure 1 (a) presents a schematic of the subwavelength birefringent waveguide-based grating structure, where the THz waves propagate along the z-axis (longitudinal direction). The waveguide-based grating is constructed by introducing the structural perturbation periodically along the propagation direction, as proposed numerically in our previous work at different frequency range [10]. The geometrical birefringence in rectangular waveguide cross- section supports two orthogonally polarized modes i.e., x-polarization (x-pol.) and y-polarization (y-pol.). As shown in the inset of Fig. 1 (a), the single grating unit consists of large (C1) and small (C2) sized rectangular cells and supports modes with effective refractive indices of neff1 and neff2, respectively. This results in periodic structural modulation due to resonant mode coupling along a longitudinal direction. Such coupling shows a stopband profile in the transmission spectrum,
Fig. 1. Schematic design and fabricated grating samples. (a) Schematic of multiple unit-cells of the subwavelength birefringent waveguide-based THz grating with the geometrical parameters (L1, L2, d1x, d1y, d2x, d2y). Inset: The unit cell cross-section consists of the large (C1) and small (C2) sized rectangular cells in the yz plane (b) Photographs of the fabricated (COC) grating samples. The number of grating periods is 29 and 45 for short (30-mm) and long (43-mm) gratings, respectively. (c) Microscopic images of the two samples for limited grating units in the yz plane.
where the Bragg frequency (fB) of the stopband can be estimated by Bragg condition as follows [10]:
where m is an integer (m= 1 in this work), c is the speed of light in vacuum, L1 and L2 are the lengths of the C1 and C2, respectively.To achieve a target frequency band at 0.15 THz, we design waveguide gratings according to Eq. (1) with appropriate cross-sectional parameters of d1x, d1y, d2x, d2y. The grating pitch ($\Lambda )$ and total grating length (period number of N) are equal to L1 + L2 and $N \times \Lambda $, respectively. We fabricated two gratings with period numbers 29 and 45. The gratings were manufactured using micromachining techniques. The photographs of the two fabricated samples are shown in Fig. 1 (b), where the total measured lengths are 30 mm (denoted as short) and 43 mm (denoted as long), respectively. The segments were machined on a Kira Super Mill M2 which is a 3-axis precision (2 µm) milling machine using a Fanuc31i controller [23]. The cutting programs used on the Kira were created using SolidCAM CAD/CAM software, which also optimized the cutting parameters. The samples were inspected using an Olympus Laser scanning microscope [24]. The microscope images of short and long samples are shown in Fig. 1 (c). To reduce propagation losses, we select a low-loss cyclic olefin copolymer (COC) material with the tradename of TOPAS COC 5013L-10 [25]. We use a COC sheet as it is relatively easier to cut the grating using the micromachining process. The thickness of the sheet is 2 mm. We utilize THz time-domain spectroscopy (THz-TDS, see details in Section 3.1) to characterize the properties of the COC. Figure 2 (a) shows the measured (experiment fitting) refractive index and absorption coefficient of COC. The index of refraction is 1.536 at 0.15 THz and constant up to 1 THz. As expected, we observe a very low absorption coefficient (0.0027 1/mm) at 0.15 THz. Based on the material properties, the extracted complex refractive index of COC at 0.15 THz is 1.538 + 0.0065i, which is used in the Lumerical FDTD simulations [26]. The measured parameters of short and long fabricated samples are summarized in Table 1. Note that the deviations represent the tolerances of the fabricated samples with respect to simulated parameters. We will discuss the impact of fabrication deviations on the performance of grating in Section 3.2.
Fig. 2. Material characterization and THz-TDS experimental setup. Measured (fitted curve) index of refraction and absorption coefficient of COC (a) and dielectric foam (b) in the frequency range from 0.1 to 1 THz. (c) Image of the fiber-coupled THz-TDS characterization setup. Inset: grating sample on a dielectric foam holder where only the waveguide edges are placed on the foam holder.
Table 1. Measured parameters of the fabricated gratings samples
3. Results and discussion
3.1 Experimental setup
We employ a THz-TDS system (Menlo TeraSmart [27]) to characterize the performance of fabricated gratings. Figure 2 (c) shows the image of the transmission characterization setup. The measured bandwidth of the THz-TDS system is from 0.1 THz to 3.5 THz with over 65 dB of dynamic range. The THz pulse is generated by the fiber-coupled THz antenna that is biased and irradiated by an ultrafast femtosecond laser. Note that the THz source and detector are linearly polarized, oriented along the y-direction in the setup. We coupled the free-space propagation of THz pulse into the grating samples by employing a pair of TPX lenses (TPX: polymethylpentene lens, with a focal length of 50 mm). Before the sample, a pinhole of 1.5 mm diameter is used, to align the grating to the center of the beam. We use a dielectric foam to hold the gratings, as shown in the inset of Fig. 2 (c). We investigate different dielectric foams and, has chosen the foam with the closet refractive index to air, [see Fig. 2(b)], which is expected to exhibit a negligible effect on the transmission properties of the gratings. The measured properties of the foam can be seen in Fig. 2 (b) which shows a refractive index of 1.004 and low losses of 0.003 1/mm in the vicinity of 0.15 THz. It should be noted that the two polarizations are measured by rotating the waveguide grating sample orthogonally. After passing through the sample under test, the beam is recollimated and focused into the detector (THz antenna) by an identical pair of lenses.
3.2 Transmission measurements
Figures 3 (a) and 3 (b) show the transmission spectra of the short and long gratings for x- and y-polarizations, where the solid and dashed curves represent the measured and numerical results, respectively. For short grating [Fig. 3(a)], the measured reflective frequencies of x- and y-polarizations are at 0.152 THz and 0.155 THz, with extinction ratios (ERs) of 5.8-dB and 5.0-dB, respectively. Note that, we consider averaged transmission outside the stopbands (green dashed line) for an approximate evaluation of experimental ERs for both polarizations. The FWHM of the stopbands are 8 (9) GHz, for x-pol. (y-pol.). For long grating [Fig. 3(b)], 8.5- and 7.5-dB ERs are observed for x-pol. and y-pol., respectively, and FWHM of 5 GHz for both polarizations. The measure reflective frequencies of long grating for x-pol. (y-pol.) are at 0.1504 (0.1528) THz. As expected, increasing the grating length leads to high ER and eventually shows strong modulation strength. This shows that the index modulation of the unit cell of the short grating is weaker than the long grating which results in different FWHMs of two gratings.
Fig. 3. Numerical computation and experimental characterization of THz birefringent fiber grating (a) Short grating (b) Long grating, transmissions for x- and y-polarizations along with extinction ratios and full-width half-maximums. Red: x-polarization, black: y-polarization, Dashed-Green: averaged-transmission level outside the stopbands, Solid-Green: extinction ratio measurement, Blue: FWHM measurement. dashed curves: simulation, solid curves: experiment.
In general, there is a good agreement between measured (solid curves in Fig. 3) and numerically calculated (dotted curves in Fig. 3) stopband positions of two gratings. The stopband positions of the short grating are the same as of numerical, while a very small deviation of 0.13% is observed between the simulation and experiment stopband of the long grating (x-pol. only). In terms of ERs and FWHMs, there is a slight mismatch in the measured results when compared to numerical simulations. For example, the x- and y-polarized experimental ERs of the short grating show mismatch of 2.2-dB and 1.5-dB, respectively. On the other hand, the ERs of the long grating illustrate a much smaller mismatch of 0.5-dB (x-pol.) and 0.2-dB (y-pol.). Furthermore, the measured FWHM is wider, particularly for short grating than the numerically calculated FHWMs, which are 5.5 and 4.5 GHz for short and long gratings, respectively. We attribute the deviations between experiment and simulation to fabrication tolerances. Obviously, the grating’s unit cells are identical in the numerical simulations, however, those of fabricated samples have slight variations (see Table 1). To understand the effect of variations on the filtering characteristics including ER and FWHMs, we numerically study the impact of the two key parameters of the grating unit structure (C1 and C2) [10]. We vary the relative fraction (L1/Λ) of C1 in the longitudinal direction and the cross-sectional parameter (dx) along the transverse (cross-sectional) direction. The numerical results suggest the reduction in ER (5-dB) and narrowing FWHM (3 GHz) of stopband for both polarization states due to weak mode coupling if the corresponding relative fraction increases (+ 50 um). This is while the decrease (- 50 um) in relative fraction can widen (5 GHz) the stopband FWHM. To improve the performance of the grating filter characteristics, we propose to change the grating design parameters ratio through structure optimization (for details, see the Supplement 1 for more details).
Furthermore, we observe low transmission (mostly for short grating) in the experimental measurements compared with simulation. We attribute that to relatively weak coupling from free space, which can be due to slight misalignment (sensitive) of the waveguide grating with an incoming THz beam. To check the effect of misalignment on the coupling efficiency, we numerically estimate the coupling efficiency of the waveguide grating using an input terahertz Gaussian beam (beam waist of 1.29 mm at 0.15 THz). The efficiency can be reduced to 47.7% for misalignment up to 0.6 mm (almost half of the cross-section dimension). To mitigate the coupling losses and eliminate the sensitivity due to alignment, we conduct two sets of measurements for each sample and in each set, we measure four points (200 µm step apart) where signal coupling into the grating is maximum (See Fig. S1 b of the Supplement 1). Note that the four points are located at the cross-section of the grating where the terahertz waves should couple into the structure. One of the advantages of the grating is that it has a large portion of the electric field in the air cladding which makes it sensitive to environmental perturbations. This also shows that our grating can also act as a sensing device. Note that all measured transmissions (Fig. 3) are normalized to the free-space signal (pinhole included). Moreover, some variations can be observed outside the stopbands mostly at low frequencies. The reason for transmission deviations at low frequencies could be that, in simulations, the refractive index of COC is from the fitted data at 0.15 THz frequency. It should be noted that we fitted the data because the measured refractive index and absorption of COC at lower frequencies have relatively large deviations.”
3.3 Group velocity dispersion
Finally, we extract the group-velocity dispersion from measured phase information of short and long gratings. To do this, we calculate the experimental GVD from the second-order derivative of the frequency-dependent propagation constant (∂2β/∂ω2) of the guided modes. Figure 4 presents the experimentally measured (solid lines) and numerically simulated (dashed lines) GVD curves of the short and long gratings. As strong index modulation of periodic subwavelength structures leads to the bandgap, the extreme variations of the group velocity at the stopband edges result in large GVD [28]. Thus, we experimentally achieve high GVDs of -25 (-25) ps/mm/THz at 0.150 (0.152) THz for short grating [Fig. 4 (a)] and -188 (-88) ps/mm/THz at 0.15 (0.151) THz for long grating [Fig. 4 (b)] of the x-pol (y-pol.) states. In numerical simulations, we note that both short and long gratings have large negative GVD values of maximum -226 (-186) ps/mm/THz and -340 (300) ps/mm/THz, respectively for x-pol (y-pol.) waves. We attribute the measured GVD deviations particularly for short grating, to its relatively flat and wide transmission (i.e., the relatively weak coupling), which implies smaller GVDs. Nevertheless, such high negative experimental GVD values have not been reported yet in THz waveguide gratings, to the best of our knowledge. Interestingly, our long-fabricated grating (Fig. 4(b)) provides more than 7.5 times larger negative GVD (GVD = -188 ps/mm/THz at 0.15 THz) in less than half of the grating length (43 mm) compared to the THz hollow-core metallic waveguide grating (GVD = -25 ps/mm/THz at 0.14 THz for the grating length of 100 mm with similar transmission losses (-11 dB) of the stopbands [5].
Fig. 4. Numerical and experimental group-velocity dispersion comparison as a function of frequency (a) Short grating, (b) Long grating. Red and black curves show x-pol. and y-pol polarizations, respectively. Note that the crossing of the gray lines in (b) represents the lowest negative GVD value (i.e., -60 ps/mm/THz) of the long grating (x-pol.) at relatively high transmission (7.8 dB) in the experimental characterization. Dashed lines: numerical, Solid lines: experiment.
Due to the large negative GVD, our fabricated devices can be useful for dispersion compensation in the THz communication system. For instance, let’s consider -60 ps/THz/mm GVD (see the crossings of grey solid lines in Fig. 4 (b)) as a typical value of our fabricated birefringent grating at f = 0.148 THz, where the transmission is also relatively high (7.8 dB attenuation compared to pass-band level). Taking 100-km long-haul backup links for satellite assisted wireless communications (generally hundreds of kilometres) as an example here (GVDs of terahertz waves in the atmosphere are 2.5 × 10−5 ps/mm/THz at 0.15 THz [5]), the required grating length for zero-GVD compensation is just 41.6 mm — similar to our fabricated long grating sample. Whereas, we also notice that the dispersion is relatively high in THz fibers with the typical values of ∼1 ps/THz/mm [5]. If we consider the THz fiber-based interconnector or backup link of 2.5 m, the same long grating (43 mm, and GVD value of -60 ps/THz/mm) could also be used for the dispersion compensation in short-range high-capacity communications [6]. Thus, high negative-dispersion in the THz waveguide-based grating can be the key device towards dispersion compensation in future THz communications systems.
4. Discussion
Table 2 summarizes the measured characteristics of the waveguide-based grating demonstrations to date in the THz frequency range. First, it shows that our COC-based fiber grating (long) achieves the highest negative GVD for both x- and y-polarization filtering compared to others. We demonstrate a large negative GVD value of -188 ps/mm/THz (x-pol.) in comparison to the GVD value of -25 ps/mm/THz of the hollow-core metallic grating. Moreover, in our case, such high GVD is achieved in less than half the grating length compared to a metallic hollow-core grating length [5]. This shows that our fabricated grating has the advantages of 7.5 times increase in GVD meanwhile in half grating length compared to reported ones, to the best of our knowledge. In nutshell, the long grating design has the optimal parameters for both dispersion compensation and filtering. It should be noted that there is a trade-off between achieving high negative GVD and high transmission in the passband.
Second, the THz grating proposed in this work is the only grating filter that can filter two orthogonal polarizations simultaneously while the others show either single-polarization or no polarization dependence at all. Interestingly, we also demonstrate the filtering of both polarizations with similar ER and FWHM. Although notch-type dielectric grating [20] and paper grating [21] may have the higher ER, it is possible to improve the ER of our grating by increasing the number of grating cells. For example, our numerical simulations show that ER could increase up to 12 dB in a grating of 59 periods, which is comparable to the ER of paper grating [21]. The FWHM of our long grating is wider than paper or notch type gratings however it is narrow than hollow-core metallic grating. The simulation shows that the minimum FWHM is 5 GHz for our proposed grating, which is reached for the grating period larger than 29. In fact, the moderate filtering frequency range could be beneficial for dispersion compensation, i.e., the design structure would be less sensitive to fabrication imperfections. It should be noted that the reason for larger FWHM of the short length is attributed to weaker modulation strength. Furthermore, we notice that a terahertz grating integrated on effective-medium-clad waveguide [11] has been demonstrated recently, yet it filters only one polarization state.
Table 2. Performance comparison of waveguide gratings in the THz regiona
5. Conclusion
In conclusion, to meet the demand for future high-speed THz communication links, we have experimentally investigated subwavelength waveguide-based THz gratings for dual-polarization filtering and dispersion compensation. Two gratings with lengths of 30 mm and 43 mm are fabricated using low-loss COC polymer by micromachining techniques. Taking advantage of the strong index modulation at the subwavelength scale, we demonstrate the highest negative GVD (7.5 times large compared to [5]) with the shortest length so far, i.e., 43 mm in comparison to 100 mm. The measurements confirm that the fabricated gratings have negative GVD of -188 ps/mm/THz and -84 ps/mm/THz for x- and y-polarizations, respectively, in a device length of only 43 mm, which can be used for dispersion compensation of more than 100-km THz wireless- and 2.5-m THz wired-communication links, using the parameters listed in Table 1 (long grating). Such dispersion compensation in a very short length demonstrates the compactness in the THz grating to the best of our knowledge. Furthermore, we experimentally characterize the propagation of the two orthogonally polarized guided modes (x- and y-polarization) at 0.15 THz, demonstrating the birefringent nature of the gratings along the propagation direction. The proposed THz grating provides polarization-maintaining filtering with the dispersion compensation functionality that can be integrated into waveguide-based THz communication systems.
Funding
National Natural Science Foundation of China (62075007); Beijing Natural Science Foundation (4192048).
Acknowledgments
This work was performed in part at the South Australia node of the Australian National Fabrication Facility. A company established under the National Collaborative Research Infrastructure Strategy to provide nano and microfabrication facilities for Australia’s researchers. The authors would like to thank Mr. Qigejian Wang and Mr. Noman Siddique from Shaghik’s Terahertz Group at UNSW for assisting with COC material characterization. S. A. acknowledges the support of UNSW Scientia funding.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data are available on request from the authors.
Supplemental document
See Supplement 1 for supporting content.
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