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Abstract
Mode-division multiplexing (MDM) has been extensively utilized to expand the capacity of chip-scale or fiber-based optical communication, whereas it is still challenging to implement the MDM for fiber-chip optical interconnects due to the huge mode mismatch between few-mode fiber (FMF) and multi-mode waveguide. In this work, we propose and design a silicon integrated six-mode edge coupler assisted with a slot waveguide, which achieves the efficient direct conversion of multiple modes between the waveguide and fiber in a broad bandwidth. Based on the principle of mode conversion, this edge coupler enables the mode conversion between six linear polarization (LP) modes (i.e. $\textrm{LP}_{\textrm{x/y}}^{\textrm{01}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11a}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11}\textrm{b}}$) in FMF and six on-chip waveguide modes (i.e. TE0, TE1, TE2, TM0, TM1, TM2) with low insertion loss, low mode crosstalk and broad bandwidth. The obtained results show that over the whole C-band the efficiency of mode conversion is higher than 98% and the mode crosstalk is low than -19 dB, while the total coupling loss is higher than 85%. The favorable results offer an important reference for designing related broadband photonic devices, and the presented scheme could be potentially exploited to further increase the transmission capability for prospective fiber-chip optical interconnections and communications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The advanced multiplexing technology for coaxial transmission of multi-channel signals is of great significance to meet the growing capacity demand of optical interconnects [1–5]. Multiple physical dimensions of photon carrier could be utilized to implement diverse multiplexing technologies, exhibiting the feasibility of high-capacity optical communication [6–8]. Wavelength-division multiplexing (WDM), time-division multiplexing (TDM), polarization-division multiplexing (PDM), advanced modulation formats, etc. all have also obtained rapid development, which continuously promote the improvement of the transmission capacity in optical communication networks [9–15]. As one of the successful technologies, mode-division multiplexing (MDM) takes advantage of multiple mode-channels to transmit different signals in a multi-mode waveguide/fiber simultaneously, which has incredibly increased the capacity of an optical communication system even to Peta-bit/s [16–19].
For the on-chip MDM systems, the integrated mode (de)multiplexer is the key device to achieve the mode efficient conversion and (de)multiplex, which also could be manufactured by the mature fabrication technologies currently [18]. Silicon photonics is regarded as one of the most excellent integrated photonic platforms due to its distinct advantages of strong light confinement, small footprint, and mature complementary metal-oxide semiconductor (CMOS) compatible technology [20]. There have numerous mode (de)multiplexers, implemented on silicon-on-insulator (SOI) platform, including adiabatic couplers, asymmetric Y-junctions, asymmetric directional couplers (ADCs), and inverse design circuits [21–24]. It is worth mentioning that on-chip mode multiplexing could be further compatible with other integrated multiplexing technologies [9–28]. The on-chip WDM-compatible MDM based on microring or Bragg grating is demonstrated on the integrated silicon platform [9,27,28]. To realize a larger capacity link, an integrated silicon 64-channel hybrid demultiplexer is proposed to implement WDM and MDM simultaneously by using arrayed-waveguide-grating wavelength multiplexer and ADC mode multiplexer [25]. Besides, MDM has also emerged as an efficient approach to further increase the transmission capability of optical fiber communications [29,30]. As one of the most popular candidates, the weakly-coupled MDM technique based on few-mode fiber (FMF) has attracted extensive attention, because FMF supporting six linear-polarized (LP) modes could avoid the difficulty of controlling higher-order modes in conventional multi-mode fibers (MMF) [30,31]. Thus, FMF with low modal crosstalk is a friendlier option for the long-reach transmission system. Although there have been plenty of works on chip-scale or fiber-based MDM technologies, a broadband and efficient coupler, as the bridge to connect on-chip multi-mode waveguide and FMF, still is a challenging task due to the mode mismatch.
To overcome the aforementioned challenge, some integrated approaches have been presented and studied to implement the multi-mode fiber-chip coupling, including vertical coupling and edge coupling. For vertical coupling, the 2D grating coupler is a common device owing to its large misalignment tolerance and small footprint [32–34]. However, the special defects of grating, i.e. limited availability of bandwidth and large insertion loss, significantly limit the application of 2D grating couplers. In comparison, the edge coupling theoretically possesses broader operation broadband, lower coupling loss, and more compact packaging. A triple-tip inverse taper with a 1 × 3 splitter has been reported for efficient four-mode coupling with a very broad bandwidth, while the number of coupling modes becomes difficult to increase in theory [35–37]. Multistage inverse taper coupler based on heterogeneous waveguide realizes the direct coupling for six guided modes, but its wavelength sensitivity impedes the compatibility of wide-band WDM [38,39]. Despite these aforementioned couplers could meet some performance requirements, it is a challenge for an on-chip coupler with more modes, low loss, low crosstalk, and broad bandwidth.
In this paper, we propose and design a multi-mode silicon integrated edge coupler by using a multistage inverse taper with polymer up-cladding, which provides a way for a direct connection between FMF and integrated multi-mode waveguide in a broad bandwidth. By introducing a nano-slot waveguide, the proposed edge coupler could achieve the broad-band mode conversion between six LP modes (i.e., $\textrm{LP}_{01}^{x/y}$, $\textrm{LP}_{11a}^{x/y}$, $\textrm{LP}_{11\textrm{b}}^{x/y}$) in FMF and six waveguide modes (i.e. TE0, TE1, TE2, TM0, TM1, TM2). Numerical simulation results show that over the C-band the efficiency of mode conversion is higher than 98% and the mode crosstalk is low than -19 dB, while the total coupling loss is higher than 85%. Such demonstration could promote the application of MDM in the fiber-chip optical interconnection networks.
2. Operation principle and structure design
Figure 1 shows the 3D structure configuration of presented silicon integrated edge coupler, which is designed on an SOI wafer with a top silicon layer, SiO2 upper-cladding, and SiO2 bottom. The presented six-mode edge coupler consists of the multistage taper assisted with a slot waveguide and the overlaid polymer nanowire waveguide. One should note that the coupler could implement broad-band and efficient mode conversion not only for the fundamental mode, but also for multiple higher-order modes. The whole schematic configuration of edge coupling is exhibited in Fig. 2(a). Figure 2 (b) is the cross section of FMF and the supporting six LP modes ($\textrm{LP}_{\textrm{x/y}}^{\textrm{01}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11a}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11}\textrm{b}}$). Figure 2 (c) is the cross section of the polymer waveguide and the supporting six guided modes (TE11, TE12, TE21, TM11, TM12, TM21). Figure 2(d) is the cross section of silicon multi-mode waveguide and the supporting six guided modes (TE0, TE1, TE2, TM0, TM1, TM2). From Fig. 2(b) and (d), one may also find the modes in FMF and multi-mode waveguide are mismatch in shape and size. Another thing worth mentioning is that two or more peaks exist in the vertical-direction field distribution of high-order fiber mode but only one peak in that of high-order waveguide mode, which greatly increases the difficulty of mode conversion. How to convert the high-order modes between FMF and multi-mode waveguide is one of the main technical concerns especially within a broad work bandwidth. With the assistance of tapered FMF, the multiple LP modes in traditional FMF (X1) could be compressed to a smaller mode spot size, as large as the cross section of the polymer waveguide (X2) [39]. Then, the polymer waveguide is directly connected to the polymer waveguide with a silicon nano-tip (X3). Finally, the multiple guide-modes could efficiently convert to the silicon waveguide modes (X4). The above modes include three modes on both two polarizations. One may also find the basically similar mode shapes of LP modes in FMF and guided-modes in polymer waveguide, which could reduce the difficulty of coupling.
Fig. 1. 3D structure configuration of silicon integrated edge coupler with a multistage slot waveguide buried in a polymer waveguide nanowire waveguide.
Fig. 2. Schematic configuration of the silicon integrated edge coupler supporting six guided-modes for fiber-chip coupling. (a) The top view of present silicon edge coupler includes a multi-stage inverse taper assisted with a multistage slot waveguide and a tapered FMF. (b) The cross section of FMF and the supporting six LP modes ($\textrm{LP}_{\textrm{x/y}}^{\textrm{01}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11a}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11}\textrm{b}}$). (c) The cross section of SU8 strip waveguide and the supporting six guided-modes (TE11, TE12, TE21, TM11, TM12, TM21). (d) The cross section of silicon multi-mode waveguide and the supporting six guided-modes (TE0, TE1, TE2, TM0, TM1, TM2).
In this coupler, the polymer waveguide plays a transitional and auxiliary role for the coupling, whose index lies between the index of Si (n Si = 3.455) and SiO2 (n SiO2 = 1.445). Apart from the polymer, some other materials such as TiO2, silicon-rich oxide (SiOx), and SiN, could be selected as an overlaid auxiliary waveguide. However, due to the limitation of fabrication technology, the growth of more thick SiN or TiO2 thin film might be not easy. The fortune is that the SU8 polymer waveguide (n SU8 = 1.574) with a larger thickness could be fabricated on SOI platform, which would be of benefit for the fabrication of SU8 strip waveguide utilized for the proposed edge coupler. The edge coupler could be fabricated by such process, shown in Fig. 3. The coupler is first patterned and etched on silicon layer through first-step E-bean lithography (EBL) and inductively coupled plasma (ICP) etching process. Subsequently, SU8 strip waveguide could be processed through spin-coated, second-step EBL, development and fixation. The different heights of polymer waveguide are obtained by adjusting the spin speeds. It is worth mentioning that the SU8 strip waveguide does not need to be etched by ICP due to its property of negative photoresist. Finally, 2-µm-thick SiO2 upper-cladding was then deposited by plasma-enhanced chemical vapor deposition (PECVD). The PECVD deposition of silicon dioxide requires a high temperature environment, which is compatible with the SU8 waveguide.
Here, the cross section of SU8 waveguide is designed to be 3 × 3 µm2, supporting at least six guide-modes. For another integrated waveguide, the width of SOI multistage silicon tapers gradually increases to convert multiple modes. One can see that the SU8 waveguide (X2) and the SU8 waveguide with a silicon nano-tip (X3) are directly connected [see Fig. 2(a)]. The coupling loss between two waveguides depends on the nano-tip width. The wider the nano tip, the larger the coupling loss [38]. Theoretically, under an ideal situation, the nano-tip width should be zero to ensure there is no facet reflection and coupling loss between two waveguides. However, the silicon nano-tip serves as the smallest structure in this coupler. The reduction of nano-tip width is limited by the minimum feature size of fabrication technology. As a result, the tip width of 60 nm is a trade-off option between the coupling loss and fabrication process [38]. The other parameters of multistage tapers could be obtained by the calculated effective index of modes, realizing that desired modes are excited and undesired modes are suppressed. In addition, to better support six waveguide modes on both two polarizations simultaneously, the height and the width of terminal bus waveguide are chosen as 340 nm and 1.2 µm, respectively.
Then, the desire is to implement the broadband and efficient mode conversion from the silicon nano-tip to the terminal waveguide, by using the silicon multistage tapers with optimal design parameter. It is particularly important and complicated for multi-mode conversion to how slowly the width of the taper varies. Here, based on the principle of mode evolution, the effective refractive index neff for the guided modes varying with waveguide width, obtained by the finite-difference method (FDM), is utilized to design the waveguide parameters. Figure 4 (a) and (c) display the calculated effective index neff for the six lowest guided-modes varying the slot waveguide and strip waveguide width, respectively. Here one should be noticed from the electric-field insets of Fig. 4 (a) that the TM11 mode of polymer waveguide with silicon nano-slot tip is quite similar to the TM0 mode of silicon slot waveguide when the waveguide width is 60 nm. It is different from the polymer waveguide (shown in Fig. 2 (c)) that the major light of the TM11 mode is basically concentrated in the silicon slot waveguide, which would cause extra loss or mode crosstalk in the direct connection between two types of polymer waveguides. In comparison, the major light of the TM11 mode (shown in the electric-field insets of Fig. 4 (c)) is distributed in the polymer waveguide for the strip waveguide, which would be to the benefit of low-loss mode conversion. Thus, here the fundamental modes rely on the multistage strip taper to achieve the conversion due to its low enough loss. The connection between strip waveguide and slot waveguide employs a mode converter with asymmetric tapers, which has sufficiently low loss for two fundamental modes [40]. While other four high order modes are converted by the assisted multistage slot waveguide to obtain a broader work bandwidth.
Fig. 4. (a) The calculated effective index neff and (d) the calculated mode polarization ratio MPR of TE polarization for the six lowest guided-modes varying the slot waveguide width from 0.06 µm to 0.7 µm, when the gap g is 120 nm. (b) The partial enlarged view for the part of 1.55 <neff < 1.57. (c) The calculated effective index neff for six lowest guided-modes as the width of silicon strip waveguide varies from 0.06 µm to 1.2µm. The insets in the upper left of (a) and (b) are the TM11 mode electric field profiles of the slot and strip waveguide, respectively, when the width of waveguide is 0.06 µm.
Such a well-known phenomenon is that the silicon waveguide with asymmetrical cross section (i.e. structure or material) in a vertical direction possesses some mode hybridization regions where two modes index curves come to be closed but still keep the anti-crossing state. According to our previous analyses, two modes with different polarizations could be completely converted to another through a taper, when the taper length is long enough to become adiabatic and the taper width range covers the hybridization regions [19]. It is deserved to notice that the mode hybridization with unstable polarization change has a high probability of introducing additional crosstalk. Thus, to avoid the possibility of increasing crosstalk, the mode hybridization needs to be controlled precisely. Mode polarization ratios (MPRs) γ x are calculated to local and evaluate the mode hybridization, which is defined as: [19,41]
Apart from the width of the segment, the taper length is a crucial parameter. Here, we used an eigenmode expansion (EME) method to calculate the mode excitation ratios η pq and simulate the light field of propagation, as shown in Fig. 5 and Fig. 6. The mode excitation ratios η pq for the i-th segment is the percentage of q-th guide mode when the p-th guide mode is launched. Considering the effect of the former segments, the mode excitation ratio is obtained not only through the individual segment but also based on former segments. Generally speaking, the tapered waveguide is long enough to be adiabatic, favoring the efficient mode excitation ratio. However, compactness requires a shorter length. Therefore, there is a trade-off consideration to determine the length to guarantee sufficient coupling efficiency and small size.
Fig. 5. The simulated mode excitation ratio ηjq of one hardest mode conversion as the taper length of the i-th segment increases.
Fig. 6. The simulated electric field profile of light propagation in the designed silicon integrated multistage tapers when six guided modes launched, respectively. (a) $\textrm{LP}_\textrm{y}^{\textrm{01}}$, (b) $\textrm{LP}_\textrm{x}^{\textrm{01}}$, (c) $\textrm{LP}_\textrm{y}^{\textrm{11a}}$, (d) $\textrm{LP}_\textrm{x}^{\textrm{11a}}$, (e) $\textrm{LP}_\textrm{y}^{\textrm{11}\textrm{b}}$, and (f) $\textrm{LP}_\textrm{x}^{\textrm{11}\textrm{b}}$.
Table 1 gives detailed structural parameters for each fragment, where the total length is 2740 µm. The simulated electric field profile of light propagation in multistage tapers is shown in Fig. 6, when six guided modes launched, respectively. The operating wavelength is 1550 nm. It could be clearly seen that the six input modes are converted successfully to the targeted on-chip waveguide modes and the six output waveguide modes have high mode purity. In addition, the mode excitation ratios for the six guided modes, exhibited in Fig. 7, shows the favorable performance over the C band. The mode conversion efficiency of six modes are higher than 98% and the mode crosstalk are lower than -21 dB in a broad band from 1530 nm to 1565 nm, indicating the mode evolution has low insert loss, low crosstalk, and broad band.
Fig. 7. Mode excitation ratios for the six guided modes when the cross section of SU8 waveguide is 3 × 3 µm2. (a) $\textrm{LP}_\textrm{x}^{\textrm{01}}$, (b) $\textrm{LP}_\textrm{x}^{\textrm{11a}}$, (c) $\textrm{LP}_\textrm{x}^{\textrm{11}\textrm{b}}$, (d) $\textrm{LP}_\textrm{y}^{\textrm{01}}$, (e) $\textrm{LP}_\textrm{y}^{\textrm{11a}}$, and (f) $\textrm{LP}_\textrm{y}^{\textrm{11}\textrm{b}}$.
Table 1. The detailed structure parameters of all the segments when the cross section of SU8 waveguide is 3 × 3 µm2.
In order to improve fiber-chip coupling efficiency, the cross section of polymer waveguide could be enlarged to 6 × 6 µm2. The larger cross section also lowers the design requirements of tapered FMF. Using the same approach, the efficient multi-mode conversion is reimplemented in the silicon multistage taper assisted with slot waveguide, when the cross section of polymer waveguide is 6 × 6 µm2. It is obvious that mode conversion is more difficult for larger size overlaid auxiliary coupling waveguide due to mode mismatch in size. Another reason is that the larger polymer waveguide could support more modes, and the corresponding mode effective index curves are closer. Therefore, the other undesired modes will excite in the progress of mode evolution after one input mode propagating through the multistage taper. This results in impurity output mode and increased mode crosstalk. To solve the problem, more segments and longer coupling length are needed to obtain a high coupling efficiency and a pure output mode. The detailed structure parameters of redesigned multistage tapers with 6 × 6 µm2 SU8 waveguide are listed in Table 2. One can clearly notice that the taper is divided into twenty-five segments and the total length of multistage tapers is 11690 µm. Figure 8 shows the mode excitation ratios for the six guided modes when the cross section of SU8 waveguide is 6 × 6 µm2, demonstrating mode conversion efficiency of > 98% and mode crosstalk of > -19 dB over the whole C band. As analysed above, mode crosstalk of larger size polymer waveguide has decreased slightly, attributed to their closer mode effective refractive index and the undesired mode excitation.
Fig. 8. Mode excitation ratios for the six guided modes when the cross section of SU8 waveguide is 6 × 6 µm2. (a) $\textrm{LP}_\textrm{x}^{\textrm{01}}$, (b) $\textrm{LP}_\textrm{x}^{\textrm{11a}}$, (c) $\textrm{LP}_\textrm{x}^{\textrm{11}\textrm{b}}$, (d) $\textrm{LP}_\textrm{y}^{\textrm{01}}$, (e) $\textrm{LP}_\textrm{y}^{\textrm{11a}}$, and (f) $\textrm{LP}_\textrm{y}^{\textrm{11}\textrm{b}}$.
Table 2. The detailed structure parameters of all the segments when the cross section of SU8 waveguide is 6 × 6 µm2.
Figure 9 displays the fabrication tolerance for mode conversion ratios by scanning the silicon multistage waveguides width (which also causes gap distance variations). Compared with that of high-order mode, the performance degradation of the fundamental mode is very small. In addition, one can see that the calculated conversion ratios are always below 0.5 dB when the waveguide width is controlled within the fabrication error variations of ±10 nm. Although such fabrication tolerance is challenging for commercial silicon photonics foundries, the high-accuracy EBL technology could be competent for the fabrication of this edge coupler. Moreover, the fabrication processes also would slightly affect the working performance of actual device, such as the extra propagation loss caused by sidewall roughness of waveguide.
Fig. 9. Fabrication tolerance to deviation of silicon waveguide width for the six guided modes when the cross section of SU8 waveguide is 6 × 6 µm2.
Furthermore, in order to fully evaluate the overall performance of the device, the insertion loss also includes fiber-to-chip losses (eg, tapered fiber to FMF, tapered fiber to chip). It is known that a sufficiently long tapered fiber can reduce the spot size of a set of modes to a certain size with low loss. In addition, the output port of tapered fiber and overlaid polymer waveguide satisfy the spot size matching condition, which is also beneficial for lowing coupling loss. When the cross section of SU8 waveguide is 6 × 6 µm2, the simulated coupling efficiencies of six lowest LP modes from FMF (X1) into the tip silicon waveguide (X3), shown in Fig. 10, displays that the coupling efficiencies for six LP modes are larger than 88% over the whole C band, where coupling efficiencies for two LP01 modes are higher than 94%. Similar to other edge couplers, the fabrication processes and experimental test also will slightly affect the working performance of actual device.
Fig. 10. Simulated coupling efficiencies of six lowest LP modes from the traditional FMF (X1) into the tip silicon waveguide (X3) when the cross section of SU8 waveguide is 6 × 6 µm2.
In Table 3, we summarize the performances of the reported state-of-the-art multi-mode couplers. Based on the vertical coupling grating method, the grating coupler is limited by specific defects of grating, such as high loss and narrow bandwidth. For edge coupling method, the triple-tip inverse taper could achieve a broad-band mode conversion for only four modes. Alternatively, another edge coupling structure is the multi-stage inverse taper, which supports more modes but a narrow bandwidth. Based on the mode evolution principle, this coupler requires a long enough length to guarantee the multi-mode conversion. However, apart from the device length, the obtained simulated result has indicated that our structure provides low loss, low crosstalk, more modes and broad bandwidth. Such interesting structure paves the way to develop the optic interconnection between FMF and chip.
Table 3. Summary of the reported state-of-the-art multi-mode silicon couplers.
3. Conclusion
In summary, we propose and design a multi-mode coupler which enables the direct coupling of multiple guided modes from the FMF to the multi-mode waveguide on the SOI platform. Compared with the multistage tapers ever reported, the structure introducing nano-slot could realize the efficient mode coupling and conversion of multiple higher-order modes in a large bandwidth. Depending on the size of the polymer overlying the tapers, we give two design parameters, both of which can achieve the direct conversion between the six LP modes ($\textrm{LP}_{\textrm{x/y}}^{\textrm{01}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11a}}$, $\textrm{LP}_{\textrm{x/y}}^{\textrm{11}\textrm{b}}$) in FMF and the waveguide modes (TE0, TE1, TE2, TM0, TM1, TM2). Numerical simulations show that the silicon multistage designed with 3 × 3 µm2 and 6 × 6 µm2 SU8 waveguide both have the high mode conversion efficiency of > 98% and the low mode crosstalk of > -19 dB in C band. On the other hand, the coupling efficiency between the conventional FMF and the polymer waveguide is also simulated, and the coupling efficiency could reach more than 87%. To the best of our knowledge, the proposed multi-mode coupler is the multistage-taper coupler with largest bandwidth ever reported. Hence, this demonstration provides a possibility of realizing the hybrid multiplexing of MDM and WDM in the FMF-chip system, further increasing the capacity of optical communication.
With further improvement, some existing challenges and related solutions toward a complete and comprehensive multi-mode edge coupler could be considered as follows.
- (1) The proposed edge coupler utilizes the tapered FMF to decrease the mode spot size and improve the coupling efficiency. If the cross section of polymer waveguide could be enlarged to the similar size of conventional FMF, such an edge coupler does not need the assist of taper or lensed fiber. Meanwhile the larger cross-section size of polymer waveguide might increase complexity of the silicon waveguide. But this deficiency could be further avoided by the multi-layer or nonlinear vertical taper structures [42,43].
- (2) Based on the mode evolution principle, the mode shape conversion with multistage waveguide tapers requires enough long device length to guarantee enough high mode purity. Although the commercial feasibility of the proposed multi-mode coupler is inevitably limited in terms of footprint, the multi-mode bend waveguide has made great progress recently, which could modify the footprint by the means of coiling the device [44,45]. On the other hand, more attention should be paid to reduce the device length of such edge multi-mode couplers in the future.
- (3) This edge coupler adopts the conventional edge coupling method, which requires accuracy alignment conditions to obtain favorable performance. However, benefiting from the spot size matching condition with the tapered fiber and SU8 waveguide, the alignment tolerance could be improved to a certain degree, especially for the coupled LP11 modes. Furthermore, the alignment tolerance also could be improved by using the larger cross section polymer waveguide.
Funding
National Key Research and Development Program of China (2019YFB2203604); National Natural Science Foundation of China (62125503, 62261160388); the Key R&D Program of Hubei Province of China (2020BAA007, 2020BAB001); the Key R&D Program of Guangdong Province (2018B030325002); the Science and Technology Innovation Commission of Shenzhen (JCYJ20200109114018750); Fundamental Research Funds for the Central Universities (2019kfyRCPY037).
Disclosures
The authors declare no conflicts of interest.
Data availability
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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