Densely packed waveguide array (DPWA) on a silicon chip for mode division multiplexing Liu Liu* SCNU-ZJU Joint Research Center of Photonics, Centre for Optical and Electromagnetic Research, South China Academy of Advanced Optoelectronics, Science Building No. 5, South China Normal University, Higher-Education Mega-Center, Guangzhou 510006, China * [email protected]
Abstract: A densely packed waveguide array (DPWA) structure for mode division multiplexing on a silicon chip is proposed. The DPWA consists of several narrow waveguides with different widths, which are densely packed with gaps of 100nm. The lateral dimension of the DPWA is comparable to the conventional multimode waveguide used for mode division multiplexing on silicon. An efficient and parallel (de)multiplexing structure is proposed. For a three-mode DPWA with a 15μm-long (de)multiplexing structure, insertion losses of –0.05dB and cross-talks of –20dB are achievable for all the modes in a wide wavelength range. The present DPWA favors a compact direct bending. In a 45μm-radius 90° bend, insertion losses of –0.1dB and cross-talks of –20dB are obtained. The proposed DPWA structure also shows a large fabrication tolerance. ©2015 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (030.4070) Modes; (060.4230) Multiplexing.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, and C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013). D. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014). J. B. Driscoll, C. P. Chen, R. R. Grote, B. Souhan, J. I. Dadap, A. Stein, M. Lu, K. Bergman, and R. M. Osgood, Jr., “A 60 Gb/s MDM-WDM Si photonic link with < 0.7 dB power penalty per channel,” Opt. Express 22(15), 18543–18555 (2014). L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014). J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightwave Technol. 31(4), 554–562 (2013). S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). Y. Kawaguchi and K. Tsutsumi, “Mode multiplexing and demultiplexing devices using multimode interference couplers,” Electron. Lett. 38(25), 1701–1702 (2002). T. Uematsu, Y. Ishizaka, Y. Kawaguchi, K. Saitoh, and M. Koshiba, “Design of a compact two-mode multi/demultiplexer consisting of multi-mode interference waveguides and a wavelength insensitive phase shifter for mode-division multiplexing transmission,” J. Lightwave Technol. 30(15), 2421–2426 (2012). J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, “Asymmetric Y junctions in silicon waveguides for on-chip mode-division multiplexing,” Opt. Lett. 38(11), 1854–1856 (2013). J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett. 38(17), 3468–3470 (2013). D. Dai, J. Wang, and Y. Shi, “Silicon mode (de) multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013). H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013). J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12135
15. D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-divisionmultiplexed optical interconnects,” Prog. Electromagn. Res. 143, 773–819 (2013). 16. L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012). 17. D. Dai, “Multimode optical waveguide enabling microbends with low inter-mode crosstalk for modemultiplexed optical interconnects,” Opt. Express 22(22), 27524–27534 (2014). 18. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997). 19. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011). 20. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com. 21. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010). 22. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). 23. G. Fan, R. Orbtchouk, B. Han, X. Liu, and Z. Zhen, “Improved coupling technique of ultracompact ring resonators in silicon-on-insulator technology,” Appl. Opt. 51(21), 5212–5215 (2012). 24. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (John Wiley & Sons, 1991).
1. Introduction Following the recent success of spatial division multiplexing (SDM) or mode division multiplexing (MDM) in fiber communications [1], this type of technology has also drawn a lot of interests in integrated photonics. The interconnect capacity can be increased by times through using a multimode waveguide [2–5]. On silicon-on-insulator (SOI) platform, for example, this can be achieved through increasing the width of the bus waveguide to a few micro-meters. This is very attractive considering fabrication technology, since such a wider waveguide nearly come at no cost. As compared to the case in fiber based systems, MDM is largely pushed by recent development of the enabling technology of multi-core and few-mode fibers [6, 7]. However, in order for MDM to impact in future on-chip and off-chip optical interconnect systems, a highly-integrated and robust solution for (de)multiplexing is necessary, since a large portion of existing integrated photonic components are still designed for single mode waveguides. Although lots of implementations have been demonstrated to address this issue [5, 8–14], (de)multiplexing is still one of the most challenging parts for MDM on chip. Another important issue is the on-chip routing of the multimode bus waveguide. Similar to the case of a multimode fiber, a sharp bending in a multimode waveguide will result in interference between the supported modes, and hence a large crosstalk between the information channels carried on them [15]. By using a sophisticated design procedure [16] or a vertical multimode waveguide [17], it is possible to achieve a compact bend. However, they come at a price of complicated fabrications including gray-scale lithography or high-aspect ratio etching of silicon, which is not commonly available in complementary metal oxide semiconductor fabrication technology. In this paper, we propose a densely packed waveguide array (DPWA) structure for MDM on a silicon chip. Instead of using one wide multimode waveguide, the proposed DPWA consists of several narrow SOI wire waveguides with different widths. Since these waveguides are densely packed with gaps of only 100nm, the effective width of the DPWA bus waveguide is comparable with the conventional multimode waveguide. An efficient and parallel (de)multiplexing scheme with a wide working wavelength range is proposed and analyzed. The bending performance of the present DPWA is also studied. 2. Basic structure and mode property The idea of the structure proposed here comes from the well-know SDM scheme, as shown in Fig. 1(a), where optical signals are carried in different waveguides which run in parallel. This type of multiplexing is the easiest way to scale up the aggregated communication capacity from one point to another. However, one crucial problem of the SDM is that the parallel waveguides cannot be placed very closely since the optical modes, in this case, will start coupling to each other. Physically, the guided modes in the coupled waveguides have no
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12136
longer well separate optical fields residing in respective waveguides. Instead, the guided mode set becomes the so-called “super-mode” [18] where different orders of modes, as shown in Fig. 1(b), all have a large amount of optical power in multiple waveguides (assuming the waveguides have the same structure), and they are distinguished only by the symmetry properties. This poses a difficulty in coupling or demultiplexing the “super-mode” to the conventional fundamental mode supported in a single waveguide. Although adiabatic tapers can be employed to achieve a high coupling efficiency, the footprint of the device is largely compromised [11].
Fig. 1. Schematic structures and mode field distributions of (a) the conventional SDM when the three waveguides are far from each other, (b) the conventional SDM when the three waveguides are close to each other, and (c) the proposed DPWA where the three waveguides are of different widths. The gray rectangles indicate waveguides. The red curves indicate the corresponding mode fields.
Fig. 2. Effective refractive indices neff for TE modes in an SOI wire waveguide (sketched in the inset) at different widths w. Here, h = 220nm. All data is for wavelength at 1.55μm.
If there would exist a coupled-waveguide structure such that the “super-mode” of this structure can still match the mode profiles of individual waveguides, it would release the difficulties mentioned above. Even a simple direct butt-coupling can be used for (de)multiplexing. This could be achieved by using such a structure where the effective refractive index of each single-waveguide mode differs significantly from others. In the SOI platform specifically, this can be done by using waveguides with different widths, as shown in Fig. 1(c). It is worthwhile to note that a similar principle has been utilized to achieve the polarization splitting function discussed in [19]. Figure 2 plots the effective refractive indices neff for trans-electric (TE) modes of a conventional 220nm-thick SOI wire waveguide surrounded all by silica at different widths w. One can find that neff of the fundamental TE mode changes fast with respect to the width, which is important to fulfill the condition about the effective-refractive-index difference described above. As an example, we build a threewaveguide DPWA, and the widths for the waveguides here are chosen to be 500nm, 408nm,
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12137
and 350nm, respectively. These widths give an equal spacing for the corresponding neff as marked in Fig. 2. Figure 3(a) shows the schematic cross-section of the proposed DPWA, where the gaps g between the waveguides are assumed the same. Figures 3(b)–3(d) show the Ex field profiles (i.e., the dominant part) of the three lowest order TE modes (named as DPWA1–DPWA3) in a DPWA with g = 100nm [20]. One can find that even if the three waveguides are packed very close to each other in this case, the optical mode of the whole structure still has a distinguishable positional distribution which corresponds to the location of each individual waveguide. Note that for the case of w1 = 500nm the single SOI waveguide is no longer single mode. However, as shown in Fig. 2, the effective refractive index of the first high-order mode is far from those of the three target modes. Thus, practically this high-order mode would not be excited. With the above parameters, the effective width of the whole DPWA, i.e., w1 + w2 + w3 + 2 × g, is 1.458μm, which is similar to the widths of multimode SOI waveguides with three modes used in the previous MDM demonstrations on silicon [5, 15].
Fig. 3. (a) Cross-sectional sketch of the DPWA with three waveguides. (b-d) Normalized amplitude distributions of the Ex fields of the three lowest-order TE modes. All data is for wavelength at 1.55μm.
3. (De)multiplexing structure An intuitive strategy for (de)multiplexing is to use a direct butt-coupling as shown in Fig. 4(a), where the three modes are (de)multiplexed simultaneously. Figures 4(b) and 4(c) shows the simulated coupling coefficients to the three DPWA modes when input from each individual waveguide. Here, we mark the coupling coefficient as Ti-j, where i = w1–w3 stands for the input mode from the individual waveguide, and j = DPWA1–DPWA3 stands for the output mode in the DPWA. One can find that the as the gap g decreases the desirable coupling coefficients (insertion losses in this case) decrease and other coefficients (cross-talks in this case) increases. For the case g = 100nm which we used in the previous section, the desirable coupling can suffer –1dB loss, while the cross-talks can go more than –10dB. In order to improve the multiplexing performance, we may employ a taper structure where the gap g is linearly tapered up to a larger value gout before connecting to the individual waveguides as shown in Fig. 5(a). Here, gout = 400nm is chosen, where the insertion losses are better than –0.05dB and the cross-talks are smaller than –20dB according to Figs. 4(b) and 4(c). Figures 5(b) and 5(c) shows the simulated coupling coefficients as the taper length varies. One can find that a very short taper, for example 15μm, is necessary to maintain low insertion losses (–0.05dB) and small cross-talks (–20dB) in order to couple light into the DPWA with g = 100nm. For demultiplexing, the insertion losses and the cross-talks show the same performance as those for multiplexing due to reciprocity, since the mode-to-mode
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12138
coupling is considered here [20]. Figure 6 illustrates pictures of the light propagation in both the multiplexing and the demultiplexing directions for the DPWA, which demonstrates the efficiency of the proposed structure. Clearly, This parallel (de)multiplexer is more compact as compared to conventional serial schemes employing directional couplers or ring resonators [5, 12]. Furthermore, in cases where lateral dimension of the bus is not strict, one can use a short taper (or even eliminate it) and a DPWA of a larger gap, e.g., g = 400nm which gives an effective width of 2.058μm.
Fig. 4. (a) Sketch of the direct butt-coupling multiplexing structure of the DPWA. (b) Insertion losses and (c) cross-talks of the structure with different gaps g. All data is for wavelength at 1.55μm. Insets show the reduced structures for simulation where the access waveguides for other modes are removed.
Fig. 5. (a) Sketch of the direct butt-coupling multiplexing structure of the DPWA with a lineartaper section. (b) Insertion losses and (c) cross-talks of the structure with different taper
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12139
lengths L. Here, g = 100nm, gout = 400nm. All data is for wavelength at 1.55μm. Insets show the reduced structures for simulation where the access waveguides for other modes are removed.
Fig. 6. Intensity profiles of the light propagation in the multiplexing and the demultiplexing directions of the proposed DPWA. For all pictures, light is input from the left.
As one can see from the above discussions, the (de)multiplexer structure adopted here is eventually based on adiabatic tapers. Thus, the working wavelength bandwidth and the fabrication tolerance of the proposed (de)multiplexer are expected to be wide. The wavelength responses of the 15μm-long multiplexer are analyzed as shown in Fig. 7. One can see that the performance of –0.05dB insertion losses and –20dB cross-talks is maintained across a wavelength range of 100nm. The fabrication tolerance of the proposed structure is also studied as shown in Fig. 8. A variation Δw of ± 20nm in the waveguide width would have a trivial impact on the performance of the (de)multiplexer. Such fabrication accuracy can be easily achieved by the state-of-the-art fabrication technology [21].
Fig. 7. Wavelength responses of the multiplexing structure for (a) insertion losses and (b) cross-talks in a 100nm band centered at 1.55μm. Here, g = 100nm, gout = 400nm, L = 15μm.
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12140
Fig. 8. (a) Simulation model for the fabrication tolerance analysis. (b) Insertion losses and (c) cross-talks when the widths of the waveguides deviate from the designed values. Here, g = 100nm, gout = 400nm, L = 15μm.
4. Bending performance Due to the efficient and compact (de)multiplexing, an immediate solution for bending in the proposed structure is to demultiplex DPWA into single waveguides, bend them, and multiplex back to DPWA, as shown in Fig. 9(a). Assuming the minimal bending radius of a conventional single-mode SOI waveguide to be 2μm [22], the whole 90° bending in Fig. 9(a) would take about 25μm × 25μm space. Nevertheless, it is still necessary to investigate how the DPWA performs under direct bending, since this approach might be used for a smallangle bend. The simulated coupling coefficients of the present DPWA through a 90° bend at different bending radii R are shown in Figs. 9(b) and 9(c), where the mode transition between the straight and the bending sections, as well as the radiative bending losses (which is negligible as compared to the impact of the mode transition within the parameter range chosen here), is considered. Here, we use a positive or negative bending radius to represent the bending towards the narrower (i.e., w3) or the wider (i.e., w1) waveguide, respectively, and only bending radii larger than 10μm, i.e., |R|>10μm, are considered. A similar terminology as that in the previous section is adopted here to mark different coefficients, except that the involved modes in this case are all DPWA modes. As one can see, the performance of the bending depends largely on the bending directions. In the positive-bending direction, a radius >30μm can give insertion losses better than –0.1dB and cross-talks lower than –20dB. On the other hand, the same performance is reached with a radius >45μm in the negative-bending direction. This is due to the fact that the conformal bending section maps the mode at the outer position of the bend to a higher linear effective refractive index. In the negative-bending case, this effect makes neff of the three modes in the DPWA move towards each other, which increases the coupling between them. Thus, high mode transition losses are expected even at a large bending radius. This negative bending scenario shown here has been utilized to enhance the coupling efficiency between an SOI ring resonator and a bent bus waveguide [23]. From the above discussions, one may conclude that the proposed DPWA structure can provide sharper bending as compared to the conventional multimode waveguide [15, 16]. However, it is worthwhile to note that for a large-angle bending it might be still preferable to use the structure shown in Fig. 9(a).
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Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12141
Fig. 9. (a) One solution to 90° bending of DPWA. (b) Insertion losses and (c) cross-talks of the DPWA under direct 90° bending at different bending radii R. Only three curves of cross-talks are shown, since the other three are also included due to reciprocity. Insets show the bending configurations for positive and negative R. The bending radii are relative to the center of the mid waveguide. Here, g = 100nm. All data is for wavelength at 1.55μm.
5. Discussion and conclusion Although a DPWA, which support three modes for MDM, is designed and analyzed here, the concept can be readily scaled for MDM with more modes. Intuitively, in the proposed design, the number of supported modes corresponds to the number of included waveguides. Thus, the effective width of the DPWA would scale linearly with respect to the number of modes that are needed for MDM. This relation is the same as that of the conventional MDM using a wide multimode waveguide, since the number of modes supported by a multimode waveguide also scales linearly with the width [24]. On the other hand, concerning the (de)multiplexing, a serial scheme [5, 12], where one (de)multiplexer is only responsible for one mode, is usually adopted in the conventional MDM. Thus, the footprint of a full (de)multiplexer for the conventional MDM would scale at least linearly to the number of included modes. Although in the proposed design a parallel (de)multiplexing structure is employed, the accessible range of the effective refractive index of an SOI waveguide is however defined according to Fig. 2. Thus, when more waveguides are included in the DPWA, the effective-refractive-index difference between each waveguide mode is reduced, which would increase the coupling between them. The super-modes in the DPWA would become less confined in the separate waveguides. In order to decrease the insertion losses and the cross-talks in this case, a larger gout and a longer taper would be necessary, which also increases the footprint of the (de)multiplexing structure. Detailed analyses are needed in order to compare the integration performance of the proposed DPWA and the conventional multimode waveguide when a large number of modes are involved for MDM. In conclusion, we have introduced a DPWA structure, which can be easily fabricated, and can be used as a bus waveguide for MDM on a silicon chip. By using SOI wire waveguides with different widths, we can densely pack them with gaps of 100nm. We have proposed a parallel (de)multiplexing structure for the present DPWA. Simulations show that insertion losses of –0.05dB and cross-talks of –20dB are achievable for a three-mode DPWA with a 15μm-long (de)multiplexing structure in a wide wavelength range. A 90° bend of the present
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12142
DPWA with insertion losses of –0.1dB and cross-talks of –20dB can be constructed with a 30μm radius towards the narrower waveguide and a 45μm radius towards the wider waveguide. Acknowledgment This research is partially supported by “863” project (Ministry of Science and Technology of China, #2012AA012201), National Nature Science Foundation of China (#61107020), and the Guangdong Innovative Research Team Program (#201001D0104799318).
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12143
Abstract: A densely packed waveguide array (DPWA) structure for mode division multiplexing on a silicon chip is proposed. The DPWA consists of several narrow waveguides with different widths, which are densely packed with gaps of 100nm. The lateral dimension of the DPWA is comparable to the conventional multimode waveguide used for mode division multiplexing on silicon. An efficient and parallel (de)multiplexing structure is proposed. For a three-mode DPWA with a 15μm-long (de)multiplexing structure, insertion losses of –0.05dB and cross-talks of –20dB are achievable for all the modes in a wide wavelength range. The present DPWA favors a compact direct bending. In a 45μm-radius 90° bend, insertion losses of –0.1dB and cross-talks of –20dB are obtained. The proposed DPWA structure also shows a large fabrication tolerance. ©2015 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (030.4070) Modes; (060.4230) Multiplexing.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, and C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013). D. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014). J. B. Driscoll, C. P. Chen, R. R. Grote, B. Souhan, J. I. Dadap, A. Stein, M. Lu, K. Bergman, and R. M. Osgood, Jr., “A 60 Gb/s MDM-WDM Si photonic link with < 0.7 dB power penalty per channel,” Opt. Express 22(15), 18543–18555 (2014). L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014). J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “305 Tb/s space division multiplexed transmission using homogeneous 19-core fiber,” J. Lightwave Technol. 31(4), 554–562 (2013). S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, Jr., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011). Y. Kawaguchi and K. Tsutsumi, “Mode multiplexing and demultiplexing devices using multimode interference couplers,” Electron. Lett. 38(25), 1701–1702 (2002). T. Uematsu, Y. Ishizaka, Y. Kawaguchi, K. Saitoh, and M. Koshiba, “Design of a compact two-mode multi/demultiplexer consisting of multi-mode interference waveguides and a wavelength insensitive phase shifter for mode-division multiplexing transmission,” J. Lightwave Technol. 30(15), 2421–2426 (2012). J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, “Asymmetric Y junctions in silicon waveguides for on-chip mode-division multiplexing,” Opt. Lett. 38(11), 1854–1856 (2013). J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett. 38(17), 3468–3470 (2013). D. Dai, J. Wang, and Y. Shi, “Silicon mode (de) multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013). H. Qiu, H. Yu, T. Hu, G. Jiang, H. Shao, P. Yu, J. Yang, and X. Jiang, “Silicon mode multi/demultiplexer based on multimode grating-assisted couplers,” Opt. Express 21(15), 17904–17911 (2013). J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12135
15. D. Dai, J. Wang, and S. He, “Silicon multimode photonic integrated devices for on-chip mode-divisionmultiplexed optical interconnects,” Prog. Electromagn. Res. 143, 773–819 (2013). 16. L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012). 17. D. Dai, “Multimode optical waveguide enabling microbends with low inter-mode crosstalk for modemultiplexed optical interconnects,” Opt. Express 22(22), 27524–27534 (2014). 18. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997). 19. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011). 20. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com. 21. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010). 22. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). 23. G. Fan, R. Orbtchouk, B. Han, X. Liu, and Z. Zhen, “Improved coupling technique of ultracompact ring resonators in silicon-on-insulator technology,” Appl. Opt. 51(21), 5212–5215 (2012). 24. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (John Wiley & Sons, 1991).
1. Introduction Following the recent success of spatial division multiplexing (SDM) or mode division multiplexing (MDM) in fiber communications [1], this type of technology has also drawn a lot of interests in integrated photonics. The interconnect capacity can be increased by times through using a multimode waveguide [2–5]. On silicon-on-insulator (SOI) platform, for example, this can be achieved through increasing the width of the bus waveguide to a few micro-meters. This is very attractive considering fabrication technology, since such a wider waveguide nearly come at no cost. As compared to the case in fiber based systems, MDM is largely pushed by recent development of the enabling technology of multi-core and few-mode fibers [6, 7]. However, in order for MDM to impact in future on-chip and off-chip optical interconnect systems, a highly-integrated and robust solution for (de)multiplexing is necessary, since a large portion of existing integrated photonic components are still designed for single mode waveguides. Although lots of implementations have been demonstrated to address this issue [5, 8–14], (de)multiplexing is still one of the most challenging parts for MDM on chip. Another important issue is the on-chip routing of the multimode bus waveguide. Similar to the case of a multimode fiber, a sharp bending in a multimode waveguide will result in interference between the supported modes, and hence a large crosstalk between the information channels carried on them [15]. By using a sophisticated design procedure [16] or a vertical multimode waveguide [17], it is possible to achieve a compact bend. However, they come at a price of complicated fabrications including gray-scale lithography or high-aspect ratio etching of silicon, which is not commonly available in complementary metal oxide semiconductor fabrication technology. In this paper, we propose a densely packed waveguide array (DPWA) structure for MDM on a silicon chip. Instead of using one wide multimode waveguide, the proposed DPWA consists of several narrow SOI wire waveguides with different widths. Since these waveguides are densely packed with gaps of only 100nm, the effective width of the DPWA bus waveguide is comparable with the conventional multimode waveguide. An efficient and parallel (de)multiplexing scheme with a wide working wavelength range is proposed and analyzed. The bending performance of the present DPWA is also studied. 2. Basic structure and mode property The idea of the structure proposed here comes from the well-know SDM scheme, as shown in Fig. 1(a), where optical signals are carried in different waveguides which run in parallel. This type of multiplexing is the easiest way to scale up the aggregated communication capacity from one point to another. However, one crucial problem of the SDM is that the parallel waveguides cannot be placed very closely since the optical modes, in this case, will start coupling to each other. Physically, the guided modes in the coupled waveguides have no
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12136
longer well separate optical fields residing in respective waveguides. Instead, the guided mode set becomes the so-called “super-mode” [18] where different orders of modes, as shown in Fig. 1(b), all have a large amount of optical power in multiple waveguides (assuming the waveguides have the same structure), and they are distinguished only by the symmetry properties. This poses a difficulty in coupling or demultiplexing the “super-mode” to the conventional fundamental mode supported in a single waveguide. Although adiabatic tapers can be employed to achieve a high coupling efficiency, the footprint of the device is largely compromised [11].
Fig. 1. Schematic structures and mode field distributions of (a) the conventional SDM when the three waveguides are far from each other, (b) the conventional SDM when the three waveguides are close to each other, and (c) the proposed DPWA where the three waveguides are of different widths. The gray rectangles indicate waveguides. The red curves indicate the corresponding mode fields.
Fig. 2. Effective refractive indices neff for TE modes in an SOI wire waveguide (sketched in the inset) at different widths w. Here, h = 220nm. All data is for wavelength at 1.55μm.
If there would exist a coupled-waveguide structure such that the “super-mode” of this structure can still match the mode profiles of individual waveguides, it would release the difficulties mentioned above. Even a simple direct butt-coupling can be used for (de)multiplexing. This could be achieved by using such a structure where the effective refractive index of each single-waveguide mode differs significantly from others. In the SOI platform specifically, this can be done by using waveguides with different widths, as shown in Fig. 1(c). It is worthwhile to note that a similar principle has been utilized to achieve the polarization splitting function discussed in [19]. Figure 2 plots the effective refractive indices neff for trans-electric (TE) modes of a conventional 220nm-thick SOI wire waveguide surrounded all by silica at different widths w. One can find that neff of the fundamental TE mode changes fast with respect to the width, which is important to fulfill the condition about the effective-refractive-index difference described above. As an example, we build a threewaveguide DPWA, and the widths for the waveguides here are chosen to be 500nm, 408nm,
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12137
and 350nm, respectively. These widths give an equal spacing for the corresponding neff as marked in Fig. 2. Figure 3(a) shows the schematic cross-section of the proposed DPWA, where the gaps g between the waveguides are assumed the same. Figures 3(b)–3(d) show the Ex field profiles (i.e., the dominant part) of the three lowest order TE modes (named as DPWA1–DPWA3) in a DPWA with g = 100nm [20]. One can find that even if the three waveguides are packed very close to each other in this case, the optical mode of the whole structure still has a distinguishable positional distribution which corresponds to the location of each individual waveguide. Note that for the case of w1 = 500nm the single SOI waveguide is no longer single mode. However, as shown in Fig. 2, the effective refractive index of the first high-order mode is far from those of the three target modes. Thus, practically this high-order mode would not be excited. With the above parameters, the effective width of the whole DPWA, i.e., w1 + w2 + w3 + 2 × g, is 1.458μm, which is similar to the widths of multimode SOI waveguides with three modes used in the previous MDM demonstrations on silicon [5, 15].
Fig. 3. (a) Cross-sectional sketch of the DPWA with three waveguides. (b-d) Normalized amplitude distributions of the Ex fields of the three lowest-order TE modes. All data is for wavelength at 1.55μm.
3. (De)multiplexing structure An intuitive strategy for (de)multiplexing is to use a direct butt-coupling as shown in Fig. 4(a), where the three modes are (de)multiplexed simultaneously. Figures 4(b) and 4(c) shows the simulated coupling coefficients to the three DPWA modes when input from each individual waveguide. Here, we mark the coupling coefficient as Ti-j, where i = w1–w3 stands for the input mode from the individual waveguide, and j = DPWA1–DPWA3 stands for the output mode in the DPWA. One can find that the as the gap g decreases the desirable coupling coefficients (insertion losses in this case) decrease and other coefficients (cross-talks in this case) increases. For the case g = 100nm which we used in the previous section, the desirable coupling can suffer –1dB loss, while the cross-talks can go more than –10dB. In order to improve the multiplexing performance, we may employ a taper structure where the gap g is linearly tapered up to a larger value gout before connecting to the individual waveguides as shown in Fig. 5(a). Here, gout = 400nm is chosen, where the insertion losses are better than –0.05dB and the cross-talks are smaller than –20dB according to Figs. 4(b) and 4(c). Figures 5(b) and 5(c) shows the simulated coupling coefficients as the taper length varies. One can find that a very short taper, for example 15μm, is necessary to maintain low insertion losses (–0.05dB) and small cross-talks (–20dB) in order to couple light into the DPWA with g = 100nm. For demultiplexing, the insertion losses and the cross-talks show the same performance as those for multiplexing due to reciprocity, since the mode-to-mode
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12138
coupling is considered here [20]. Figure 6 illustrates pictures of the light propagation in both the multiplexing and the demultiplexing directions for the DPWA, which demonstrates the efficiency of the proposed structure. Clearly, This parallel (de)multiplexer is more compact as compared to conventional serial schemes employing directional couplers or ring resonators [5, 12]. Furthermore, in cases where lateral dimension of the bus is not strict, one can use a short taper (or even eliminate it) and a DPWA of a larger gap, e.g., g = 400nm which gives an effective width of 2.058μm.
Fig. 4. (a) Sketch of the direct butt-coupling multiplexing structure of the DPWA. (b) Insertion losses and (c) cross-talks of the structure with different gaps g. All data is for wavelength at 1.55μm. Insets show the reduced structures for simulation where the access waveguides for other modes are removed.
Fig. 5. (a) Sketch of the direct butt-coupling multiplexing structure of the DPWA with a lineartaper section. (b) Insertion losses and (c) cross-talks of the structure with different taper
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12139
lengths L. Here, g = 100nm, gout = 400nm. All data is for wavelength at 1.55μm. Insets show the reduced structures for simulation where the access waveguides for other modes are removed.
Fig. 6. Intensity profiles of the light propagation in the multiplexing and the demultiplexing directions of the proposed DPWA. For all pictures, light is input from the left.
As one can see from the above discussions, the (de)multiplexer structure adopted here is eventually based on adiabatic tapers. Thus, the working wavelength bandwidth and the fabrication tolerance of the proposed (de)multiplexer are expected to be wide. The wavelength responses of the 15μm-long multiplexer are analyzed as shown in Fig. 7. One can see that the performance of –0.05dB insertion losses and –20dB cross-talks is maintained across a wavelength range of 100nm. The fabrication tolerance of the proposed structure is also studied as shown in Fig. 8. A variation Δw of ± 20nm in the waveguide width would have a trivial impact on the performance of the (de)multiplexer. Such fabrication accuracy can be easily achieved by the state-of-the-art fabrication technology [21].
Fig. 7. Wavelength responses of the multiplexing structure for (a) insertion losses and (b) cross-talks in a 100nm band centered at 1.55μm. Here, g = 100nm, gout = 400nm, L = 15μm.
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12140
Fig. 8. (a) Simulation model for the fabrication tolerance analysis. (b) Insertion losses and (c) cross-talks when the widths of the waveguides deviate from the designed values. Here, g = 100nm, gout = 400nm, L = 15μm.
4. Bending performance Due to the efficient and compact (de)multiplexing, an immediate solution for bending in the proposed structure is to demultiplex DPWA into single waveguides, bend them, and multiplex back to DPWA, as shown in Fig. 9(a). Assuming the minimal bending radius of a conventional single-mode SOI waveguide to be 2μm [22], the whole 90° bending in Fig. 9(a) would take about 25μm × 25μm space. Nevertheless, it is still necessary to investigate how the DPWA performs under direct bending, since this approach might be used for a smallangle bend. The simulated coupling coefficients of the present DPWA through a 90° bend at different bending radii R are shown in Figs. 9(b) and 9(c), where the mode transition between the straight and the bending sections, as well as the radiative bending losses (which is negligible as compared to the impact of the mode transition within the parameter range chosen here), is considered. Here, we use a positive or negative bending radius to represent the bending towards the narrower (i.e., w3) or the wider (i.e., w1) waveguide, respectively, and only bending radii larger than 10μm, i.e., |R|>10μm, are considered. A similar terminology as that in the previous section is adopted here to mark different coefficients, except that the involved modes in this case are all DPWA modes. As one can see, the performance of the bending depends largely on the bending directions. In the positive-bending direction, a radius >30μm can give insertion losses better than –0.1dB and cross-talks lower than –20dB. On the other hand, the same performance is reached with a radius >45μm in the negative-bending direction. This is due to the fact that the conformal bending section maps the mode at the outer position of the bend to a higher linear effective refractive index. In the negative-bending case, this effect makes neff of the three modes in the DPWA move towards each other, which increases the coupling between them. Thus, high mode transition losses are expected even at a large bending radius. This negative bending scenario shown here has been utilized to enhance the coupling efficiency between an SOI ring resonator and a bent bus waveguide [23]. From the above discussions, one may conclude that the proposed DPWA structure can provide sharper bending as compared to the conventional multimode waveguide [15, 16]. However, it is worthwhile to note that for a large-angle bending it might be still preferable to use the structure shown in Fig. 9(a).
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12141
Fig. 9. (a) One solution to 90° bending of DPWA. (b) Insertion losses and (c) cross-talks of the DPWA under direct 90° bending at different bending radii R. Only three curves of cross-talks are shown, since the other three are also included due to reciprocity. Insets show the bending configurations for positive and negative R. The bending radii are relative to the center of the mid waveguide. Here, g = 100nm. All data is for wavelength at 1.55μm.
5. Discussion and conclusion Although a DPWA, which support three modes for MDM, is designed and analyzed here, the concept can be readily scaled for MDM with more modes. Intuitively, in the proposed design, the number of supported modes corresponds to the number of included waveguides. Thus, the effective width of the DPWA would scale linearly with respect to the number of modes that are needed for MDM. This relation is the same as that of the conventional MDM using a wide multimode waveguide, since the number of modes supported by a multimode waveguide also scales linearly with the width [24]. On the other hand, concerning the (de)multiplexing, a serial scheme [5, 12], where one (de)multiplexer is only responsible for one mode, is usually adopted in the conventional MDM. Thus, the footprint of a full (de)multiplexer for the conventional MDM would scale at least linearly to the number of included modes. Although in the proposed design a parallel (de)multiplexing structure is employed, the accessible range of the effective refractive index of an SOI waveguide is however defined according to Fig. 2. Thus, when more waveguides are included in the DPWA, the effective-refractive-index difference between each waveguide mode is reduced, which would increase the coupling between them. The super-modes in the DPWA would become less confined in the separate waveguides. In order to decrease the insertion losses and the cross-talks in this case, a larger gout and a longer taper would be necessary, which also increases the footprint of the (de)multiplexing structure. Detailed analyses are needed in order to compare the integration performance of the proposed DPWA and the conventional multimode waveguide when a large number of modes are involved for MDM. In conclusion, we have introduced a DPWA structure, which can be easily fabricated, and can be used as a bus waveguide for MDM on a silicon chip. By using SOI wire waveguides with different widths, we can densely pack them with gaps of 100nm. We have proposed a parallel (de)multiplexing structure for the present DPWA. Simulations show that insertion losses of –0.05dB and cross-talks of –20dB are achievable for a three-mode DPWA with a 15μm-long (de)multiplexing structure in a wide wavelength range. A 90° bend of the present
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12142
DPWA with insertion losses of –0.1dB and cross-talks of –20dB can be constructed with a 30μm radius towards the narrower waveguide and a 45μm radius towards the wider waveguide. Acknowledgment This research is partially supported by “863” project (Ministry of Science and Technology of China, #2012AA012201), National Nature Science Foundation of China (#61107020), and the Guangdong Innovative Research Team Program (#201001D0104799318).
#234914 - $15.00 USD © 2015 OSA
Received 18 Feb 2015; revised 22 Apr 2015; accepted 22 Apr 2015; published 29 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012135 | OPTICS EXPRESS 12143
