Abstract

In the past, multimode transmission through fibers has not been considered a preferred means of signal propagation due to the intermodal dispersion, which limits the data rate. However, recently, there has been an interest in using different modes as individual channels to increase the overall data rate. However, the challenging task in implementing such a system is that each individual mode has to be excited separately without mixing, and these should remain separated even at the bents and splices, and finally, they need to be collected separately. In this paper, design and optimization of a compact optical mode splitter by introducing a small slot in a silicon nanowire waveguide is demonstrated by employing a full-vectorial finite element method. The authors report here that by creating a slot within a waveguide, the desired coupling length ratio of 1:2 between the fundamental and the second modes can be obtained. The waveguide junctions have also been analyzed by using a rigorous least squares boundary residual method to study power transfer efficiency and effect of fabrication tolerances.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

2016 (4)

C. Pan and B. M. A. Rahman, “Accurate analysis of the mode (de) multiplexer using asymmetric directional coupler,” J. Lightwave Technol. 34(9), 2288–2296 (2016).
[Crossref]

S. L. Hada and B. M. A. Rahman, “Rigorous analysis of numerical methods: a comparative study,” Opt. Quantum Electron. 48(6), 309 (2016).
[Crossref]

W. Jiang, N. Kohli, X. Sun, and B. M. A. Rahman, “Multi-poly-silicon-layer-based spot-size converter for efficient coupling between silicon waveguide and standard single-mode fiber,” IEEE Photon. J. 8(3), 1–12 (2016).
[Crossref]

J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
[Crossref]

2015 (2)

2014 (2)

2013 (4)

2012 (1)

2011 (2)

2010 (4)

2009 (1)

2008 (1)

2007 (2)

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

C. Tsekrekos and A. Koonen, “Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link,” Opt. Lett. 32(9), 1041–1043 (2007).
[Crossref]

2006 (2)

2004 (1)

1994 (1)

B. M. A. Rahman, T. Wongcharoen, and K. T. V. Grattan, “Finite element analysis of nonsynchronous directional couplers,” Fiber Integr. Opt. 13(3), 331–336 (1994).
[Crossref]

1988 (1)

B. M. A. Rahman and J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6(1), 52–57 (1988).
[Crossref]

1985 (1)

B. M. A. Rahman and J. B. Davies, “Vector–H finite element solution of GaAs/GaAlAs rib waveguides,” IEE Proc. J. Optoelectron. 132(6), 349–353 (1985).
[Crossref]

1984 (1)

B. M. A. Rahman and J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[Crossref]

Agarwal, A.

Almeida, V. R.

Asghari, M.

Baets, R.

Barrios, C. A.

Basov, D. N.

Cao, W.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Chen, X.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Chiu, Y.-j.

Chung, Y.

Cunningham, J. E.

Da Ros, F.

Dadap, J. I.

Dai, D.

Davies, J. B.

B. M. A. Rahman and J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6(1), 52–57 (1988).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Vector–H finite element solution of GaAs/GaAlAs rib waveguides,” IEE Proc. J. Optoelectron. 132(6), 349–353 (1985).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[Crossref]

Ding, Y.

Divliansky, I. B.

Dong, P.

Dorin, B. A.

Driscoll, J. B.

Fang, Q.

Feng, D.

Fini, J. M.

Fishteyn, M.

B. Zhu, T. F. Taunay, M. F. Yan, M. Fishteyn, G. Oulundsen, and D. Vaidya, “70-Gb/s multicore multimode fiber transmissions for optical data links,” IEEE Photon. Technol. Lett. 22(22), 1647–1649 (2010).
[Crossref]

Fong, K. H.

Z. Lambak, K. Khairi, Z. Hamzah, and K. H. Fong, “Evaluation of mode filter in optical splitter by using method of lines,” in RF and Microwave Conference (RFM), 2011 IEEE International, pp. 307–310, IEEE, 2011.

Franz, Y.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Fujiwara, M.

Gao, W.

Grattan, K. T. V.

B. M. A. Rahman, T. Wongcharoen, and K. T. V. Grattan, “Finite element analysis of nonsynchronous directional couplers,” Fiber Integr. Opt. 13(3), 331–336 (1994).
[Crossref]

Grillanda, S.

Grote, R. R.

Hada, S. L.

S. L. Hada and B. M. A. Rahman, “Rigorous analysis of numerical methods: a comparative study,” Opt. Quantum Electron. 48(6), 309 (2016).
[Crossref]

S. L. Hada and B. M. A. Rahman, “Design concepts of a novel mode splitter for multimode communication systems,” in Computers and Devices for Communication (CODEC), International Conference on, pp. 1–4, IEEE, 2015.

Hamzah, Z.

Z. Lambak, K. Khairi, Z. Hamzah, and K. H. Fong, “Evaluation of mode filter in optical splitter by using method of lines,” in RF and Microwave Conference (RFM), 2011 IEEE International, pp. 307–310, IEEE, 2011.

Ho, S.-T.

Hsu, R. C.

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

B. Jalali, R. C. Hsu, and A. R. Shah, “Coherent Optical MIMO,” in Defense and Security, International Society for Optics and Photonics, pp. 121–127, 2005.

Huang, B.

Huang, Y.

Ishizaka, Y.

Jalali, B.

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

B. Jalali, R. C. Hsu, and A. R. Shah, “Coherent Optical MIMO,” in Defense and Security, International Society for Optics and Photonics, pp. 121–127, 2005.

Jia, L.

Jiang, W.

W. Jiang, N. Kohli, X. Sun, and B. M. A. Rahman, “Multi-poly-silicon-layer-based spot-size converter for efficient coupling between silicon waveguide and standard single-mode fiber,” IEEE Photon. J. 8(3), 1–12 (2016).
[Crossref]

Kawaguchi, Y.

Khairi, K.

Z. Lambak, K. Khairi, Z. Hamzah, and K. H. Fong, “Evaluation of mode filter in optical splitter by using method of lines,” in RF and Microwave Conference (RFM), 2011 IEEE International, pp. 307–310, IEEE, 2011.

Kimerling, L.

Kohli, N.

W. Jiang, N. Kohli, X. Sun, and B. M. A. Rahman, “Multi-poly-silicon-layer-based spot-size converter for efficient coupling between silicon waveguide and standard single-mode fiber,” IEEE Photon. J. 8(3), 1–12 (2016).
[Crossref]

Koonen, A.

Koshiba, M.

Krishnamoorthy, A. V.

Lai, Y.-C.

Lambak, Z.

Z. Lambak, K. Khairi, Z. Hamzah, and K. H. Fong, “Evaluation of mode filter in optical splitter by using method of lines,” in RF and Microwave Conference (RFM), 2011 IEEE International, pp. 307–310, IEEE, 2011.

Li, C.

Li, G.

Li, Y.

Liang, H.

Liao, J.

J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
[Crossref]

Liou, J.-h.

Liow, T.-Y.

Lipson, M.

Littlejohns, C. G.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Liu, M.

J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
[Crossref]

Liu, Z.

Lo, G.

Loh, T.-H.

Lu, M.

Luo, X.

Mailis, S.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Melloni, A.

Michel, J.

Milosevic, M. M.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Mookherjea, S.

Morichetti, F.

Ng, K.-T.

Oguma, M.

Osgood, R. M.

Ou, H.

Oulundsen, G.

B. Zhu, T. F. Taunay, M. F. Yan, M. Fishteyn, G. Oulundsen, and D. Vaidya, “70-Gb/s multicore multimode fiber transmissions for optical data links,” IEEE Photon. Technol. Lett. 22(22), 1647–1649 (2010).
[Crossref]

Pan, C.

Peacock, A. C.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Peucheret, C.

Qian, W.

Qiu, C.

Raghunathan, V.

Rahman, B. M. A.

S. L. Hada and B. M. A. Rahman, “Rigorous analysis of numerical methods: a comparative study,” Opt. Quantum Electron. 48(6), 309 (2016).
[Crossref]

C. Pan and B. M. A. Rahman, “Accurate analysis of the mode (de) multiplexer using asymmetric directional coupler,” J. Lightwave Technol. 34(9), 2288–2296 (2016).
[Crossref]

W. Jiang, N. Kohli, X. Sun, and B. M. A. Rahman, “Multi-poly-silicon-layer-based spot-size converter for efficient coupling between silicon waveguide and standard single-mode fiber,” IEEE Photon. J. 8(3), 1–12 (2016).
[Crossref]

B. M. A. Rahman, T. Wongcharoen, and K. T. V. Grattan, “Finite element analysis of nonsynchronous directional couplers,” Fiber Integr. Opt. 13(3), 331–336 (1994).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6(1), 52–57 (1988).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Vector–H finite element solution of GaAs/GaAlAs rib waveguides,” IEE Proc. J. Optoelectron. 132(6), 349–353 (1985).
[Crossref]

B. M. A. Rahman and J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[Crossref]

S. L. Hada and B. M. A. Rahman, “Design concepts of a novel mode splitter for multimode communication systems,” in Computers and Devices for Communication (CODEC), International Conference on, pp. 1–4, IEEE, 2015.

Reed, G. T.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Robinson, J. T.

Ruan, C.

J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
[Crossref]

Runge, A. F.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Saitoh, K.

Sayed, A. H.

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

Schrauwen, J.

Shafiiha, R.

Shah, A.

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

Shah, A. R.

B. Jalali, R. C. Hsu, and A. R. Shah, “Coherent Optical MIMO,” in Defense and Security, International Society for Optics and Photonics, pp. 121–127, 2005.

Shen, Y.

Shi, Y.

Sim, D.

Singh, V.

Soma, S.

Song, J.

Soref, R.

Souhan, B.

Sun, X.

W. Jiang, N. Kohli, X. Sun, and B. M. A. Rahman, “Multi-poly-silicon-layer-based spot-size converter for efficient coupling between silicon waveguide and standard single-mode fiber,” IEEE Photon. J. 8(3), 1–12 (2016).
[Crossref]

Suzuki, K.-I.

Taga, H.

Takushima, Y.

Tarighat, A.

A. Tarighat, R. C. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links,” IEEE Commun. Mag. 45(5), 57–63 (2007).
[Crossref]

Taunay, T. F.

J. M. Fini, B. Zhu, T. F. Taunay, and M. F. Yan, “Statistics of crosstalk in bent multicore fibers,” Opt. Express 18(14), 15122–15129 (2010).
[Crossref]

B. Zhu, T. F. Taunay, M. F. Yan, M. Fishteyn, G. Oulundsen, and D. Vaidya, “70-Gb/s multicore multimode fiber transmissions for optical data links,” IEEE Photon. Technol. Lett. 22(22), 1647–1649 (2010).
[Crossref]

Thomson, D. J.

M. M. Milosevic, X. Chen, W. Cao, A. F. Runge, Y. Franz, C. G. Littlejohns, S. Mailis, A. C. Peacock, D. J. Thomson, and G. T. Reed, “Ion implantation in silicon for trimming the operating wavelength of ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–7 (2018).
[Crossref]

Tsekrekos, C.

Tu, X.

Uematsu, T.

Vaidya, D.

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J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
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J. Liao, L. Zhang, M. Liu, L. Wang, W. Wang, G. Wang, C. Ruan, W. Zhao, and W. Zhang, “Mode splitter without changing the mode order in SOI waveguide,” IEEE Photon. Technol. Lett. 28(22), 2597–2600 (2016).
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B. Zhu, T. F. Taunay, M. F. Yan, M. Fishteyn, G. Oulundsen, and D. Vaidya, “70-Gb/s multicore multimode fiber transmissions for optical data links,” IEEE Photon. Technol. Lett. 22(22), 1647–1649 (2010).
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Fiber Integr. Opt. (1)

B. M. A. Rahman, T. Wongcharoen, and K. T. V. Grattan, “Finite element analysis of nonsynchronous directional couplers,” Fiber Integr. Opt. 13(3), 331–336 (1994).
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[Crossref]

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Figures (14)

Fig. 1.
Fig. 1. Schematic Diagram of a Mode Splitter
Fig. 2.
Fig. 2. Variations of the Propagation constant, $\beta$ with the Mesh division
Fig. 3.
Fig. 3. Variations of $L_c^{11}$ and $L_R$ with the Mesh division
Fig. 4.
Fig. 4. $L_R$ variation with the Separation ($S$)
Fig. 5.
Fig. 5. $L_R$ and $L_c^{21}$ variation with the Height for the $H^y_{21}$ Mode
Fig. 6.
Fig. 6. Cross-section of a modified Symmetrical Directional Coupler
Fig. 7.
Fig. 7. $H_y$ field variation along the x-direction: (a) $H^y_{11}$ even Supermode; (b) $H^y_{21}$ even Supermode
Fig. 8.
Fig. 8. Variation of $L_R$ with the Slot-height ($t$)
Fig. 9.
Fig. 9. Variation of $L_R$ with the Slot-width ($\delta$)
Fig. 10.
Fig. 10. $L_R$ Variation with the Offset of Slot-width Position ($\Delta$x)
Fig. 11.
Fig. 11. Variation of Coupled Power with the Slot-width ($\delta$)
Fig. 12.
Fig. 12. Variation of Coupled Power with Waveguide Width ($W$)
Fig. 13.
Fig. 13. Variation of Coupled Power with Separation ($S$)
Fig. 14.
Fig. 14. Variation of Coupled Power with Wavelength ($\lambda$)

Tables (2)

Tables Icon

Table 1. Insertion loss, Power Coupled and Cross-talk with δ -variation for the H 11 y and H 21 y modes

Tables Icon

Table 2. Insertion loss, Power Coupled and Cross-talk with t -variation for the H 11 y and H 21 y modes

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

L = m L c 11 = n L c i j
L R = L c 11 / L c i j
x = x r + 1 ( x r + 1 x r ) 2 x r + 1 2 x r + x r 1
L c = π β e β o
J = Ω | E t I E t I I | 2 + α Z 0 2 | H t I H t I I | 2 d Ω

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