Abstract

We study the correlations between the driving signal reflection on the traveling wave electrodes and the modulated signal characteristics of silicon Mach-Zehnder modulators (MZM). Correlation coefficients are introduced for systematic and quantitative analysis. The signal-to-noise ratio, extinction ratio, and bit error rate show similar correlation behaviors with the mean reflection magnitude over proper frequency ranges, whereas the correlation behaviors of the temporal parameters can be complex. Partial correlation coefficients can be introduced to help remove the influence of other factors. Some relevant fabrication variation scenarios in the underlying structures are discussed, and potential approaches to mitigating the effects of such variations are suggested.

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

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References

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2019 (1)

2018 (2)

R. Zhu, X. Zhou, N. Yang, L. M. Leng, and W. Jiang, “Towards High Extinction Ratio in Silicon Thermo-Optic Switches-Unravelling Complexity of Fabrication Variation,” IEEE Photonics J. 10(4), 1–8 (2018).
[Crossref]

M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

2017 (1)

2016 (5)

2015 (1)

2014 (5)

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

P. Dong, Y.-K. Chen, G.-H. Duan, and D. T. Neilson, “Silicon photonic devices and integrated circuits,” Nanophotonics 3(4-5), 205 (2014).
[Crossref]

H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
[Crossref]

Y. Yang, Q. Fang, M. Yu, X. Tu, R. Rusli, and G. Q. Lo, “High-efficiency Si optical modulator using Cu travelling-wave electrode,” Opt. Express 22(24), 29978–29985 (2014).
[Crossref]

X. Tu, K. F. Chang, T. Y. Liow, J. Song, X. Luo, L. Jia, Q. Fang, M. Yu, G. Q. Lo, P. Dong, and Y. K. Chen, “Silicon optical modulator with shield coplanar waveguide electrodes,” Opt. Express 22(19), 23724–23731 (2014).
[Crossref]

2013 (2)

2012 (2)

2010 (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

2008 (1)

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008).
[Crossref]

2007 (1)

W. Jiang, L. Gu, X. Chen, and R. T. Chen, “Photonic crystal waveguide modulators for silicon photonics: Device physics and some recent progress,” Solid-State Electron. 51(10), 1278–1286 (2007).
[Crossref]

2006 (2)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Abadía, N.

Anderson, T. W.

T. W. Anderson, “An introduction to multivariate statistical analysis,” (Wiley New York, 2003).

Bahrami, H.

Baudot, C.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Boeuf, F.

Bogaerts, W.

Y. F. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4(2), 93–100 (2016).
[Crossref]

H. Yu and W. Bogaerts, “An Equivalent Circuit Model of the Traveling Wave Electrode for Carrier-Depletion-Based Silicon Optical Modulators,” J. Lightwave Technol. 30(11), 1602–1609 (2012).
[Crossref]

Chagnon, M.

Chang, K. F.

Chen, H. T.

Chen, R. T.

H. Subbaraman, X. C. Xu, A. Hosseini, X. Y. Zhang, Y. Zhang, D. Kwong, and R. T. Chen, “Recent advances in silicon-based passive and active optical interconnects,” Opt. Express 23(3), 2487–2510 (2015).
[Crossref]

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008).
[Crossref]

W. Jiang, L. Gu, X. Chen, and R. T. Chen, “Photonic crystal waveguide modulators for silicon photonics: Device physics and some recent progress,” Solid-State Electron. 51(10), 1278–1286 (2007).
[Crossref]

Chen, S. W.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Chen, X.

X. Chen, M. Mohamed, Z. Li, L. Shang, and A. R. Mickelson, “Process variation in silicon photonic devices,” Appl. Opt. 52(31), 7638–7647 (2013).
[Crossref]

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008).
[Crossref]

W. Jiang, L. Gu, X. Chen, and R. T. Chen, “Photonic crystal waveguide modulators for silicon photonics: Device physics and some recent progress,” Solid-State Electron. 51(10), 1278–1286 (2007).
[Crossref]

Chen, Y. K.

Chen, Y.-K.

P. Dong, Y.-K. Chen, G.-H. Duan, and D. T. Neilson, “Silicon photonic devices and integrated circuits,” Nanophotonics 3(4-5), 205 (2014).
[Crossref]

Chrostowski, L.

Cremer, S.

Dhaene, T.

Y. F. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4(2), 93–100 (2016).
[Crossref]

Ding, J. F.

Dong, P.

Duan, G.-H.

P. Dong, Y.-K. Chen, G.-H. Duan, and D. T. Neilson, “Silicon photonic devices and integrated circuits,” Nanophotonics 3(4-5), 205 (2014).
[Crossref]

El-Fiky, E.

Fang, Q.

Fathpour, S.

Fere, M.

Flueckiger, J.

Gardes, F. Y.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Gill, D. M.

Green, W. M. J.

Gu, L.

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008).
[Crossref]

W. Jiang, L. Gu, X. Chen, and R. T. Chen, “Photonic crystal waveguide modulators for silicon photonics: Device physics and some recent progress,” Solid-State Electron. 51(10), 1278–1286 (2007).
[Crossref]

Gui, C.

Haensch, W.

Hoang, T.

Hosseini, A.

Hsu, S. S.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Hu, Y. F.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Jacques, M.

Jalali, B.

Jhoja, J.

Ji, R. Q.

Jia, L.

Jiang, W.

R. Zhu, X. Zhou, N. Yang, L. M. Leng, and W. Jiang, “Towards High Extinction Ratio in Silicon Thermo-Optic Switches-Unravelling Complexity of Fabrication Variation,” IEEE Photonics J. 10(4), 1–8 (2018).
[Crossref]

L. Gu, W. Jiang, X. Chen, and R. T. Chen, “Physical mechanism of p-i-n diode based photonic crystal silicon electrooptic modulators for gigahertz operation,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1132–1139 (2008).
[Crossref]

W. Jiang, L. Gu, X. Chen, and R. T. Chen, “Photonic crystal waveguide modulators for silicon photonics: Device physics and some recent progress,” Solid-State Electron. 51(10), 1278–1286 (2007).
[Crossref]

Klein, J.

Kwong, D.

Le Maitre, P.

Leng, L. M.

R. Zhu, X. Zhou, N. Yang, L. M. Leng, and W. Jiang, “Towards High Extinction Ratio in Silicon Thermo-Optic Switches-Unravelling Complexity of Fabrication Variation,” IEEE Photonics J. 10(4), 1–8 (2018).
[Crossref]

Li, A.

Y. F. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4(2), 93–100 (2016).
[Crossref]

Li, K.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Li, M. F.

M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

Li, R.

Li, X.

M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

Li, X. Y.

H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
[Crossref]

Li, Z.

Li, Z. Y.

H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
[Crossref]

Liow, T. Y.

Liu, A.

Lo, G. Q.

Lu, Y. Y.

Lu, Z. Q.

Luo, X.

Luo, X. S.

Maggi, L.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Mashanovich, G. Z.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Masini, G.

Mekis, A.

Mickelson, A. R.

Min, R.

Mohamed, M.

Morsy-Osman, M.

Nedeljkovic, M.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Neilson, D. T.

P. Dong, Y.-K. Chen, G.-H. Duan, and D. T. Neilson, “Silicon photonic devices and integrated circuits,” Nanophotonics 3(4-5), 205 (2014).
[Crossref]

Ning, T. H.

Y. Taur and T. H. Ning, Fundamentals of modern VLSI devices (Cambridge university press, 2009).

Orcutt, J. S.

Park, C. S.

Patel, D.

Petiton, H.

Pinguet, T.

Plant, D. V.

Pond, J.

Proesel, J. E.

Reed, G. T.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Rusch, L. A.

Rusli, R.

Saleh, B. E.

B. E. Saleh and M. C. Teich, Fundamentals of photonics (John Wiley & Sons, 1991).

Samani, A.

Sepehrian, H.

Shang, L.

Shaw, M.

Shi, W.

Sinsky, J. H.

Song, J.

Song, J. F.

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Soref, R. A.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Spina, D.

Y. F. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4(2), 93–100 (2016).
[Crossref]

Subbaraman, H.

Taur, Y.

Y. Taur and T. H. Ning, Fundamentals of modern VLSI devices (Cambridge university press, 2009).

Teich, M. C.

B. E. Saleh and M. C. Teich, Fundamentals of photonics (John Wiley & Sons, 1991).

Temporiti, E.

Thomson, D. J.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Tian, Y. H.

Traldi, M.

Tu, X.

Tu, X. G.

Vulliet, N.

Wang, L.

M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

Wang, X.

Wilson, P. R.

G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014).
[Crossref]

Xiao, X.

M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
[Crossref]

Xing, Y. F.

Y. F. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4(2), 93–100 (2016).
[Crossref]

Xiong, C.

Xu, H.

H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
[Crossref]

Xu, X. C.

Yang, L.

Yang, N.

R. Zhu, X. Zhou, N. Yang, L. M. Leng, and W. Jiang, “Towards High Extinction Ratio in Silicon Thermo-Optic Switches-Unravelling Complexity of Fabrication Variation,” IEEE Photonics J. 10(4), 1–8 (2018).
[Crossref]

Yang, Y.

Yu, H.

Yu, J. Z.

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[Crossref]

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M. F. Li, L. Wang, X. Li, X. Xiao, and S. H. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photonics Res. 6(2), 109–116 (2018).
[Crossref]

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H. Xu, X. Y. Li, X. Xiao, Z. Y. Li, Y. D. Yu, and J. Z. Yu, “Demonstration and Characterization of High-Speed Silicon Depletion-Mode Mach-Zehnder Modulators,” IEEE J. Sel. Top. Quantum Electron. 20(6), 10–16 (2014).
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[Crossref]

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R. Zhu, X. Zhou, N. Yang, L. M. Leng, and W. Jiang, “Towards High Extinction Ratio in Silicon Thermo-Optic Switches-Unravelling Complexity of Fabrication Variation,” IEEE Photonics J. 10(4), 1–8 (2018).
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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic view of the MZM and the inset is the cross-section diagram of the PN junction. (b) Microscopic image of the MZM. (c) Typical spectrum of the MZM.
Fig. 2.
Fig. 2. Experimental setup of the measurement system used to characterize the MZM. (LD: laser diode; PC: polarization controller; DUT: device under test; EDFA: erbium-doped fiber amplifier; PD: photodetector; VNA: Vector Network Analyzer; BERT: bit error rate tester; AMP: amplifier; DCA: oscilloscope.). The lower-right inset schematically illustrates signal reflection on the electrode due to imperfect impedance matching at the termination.
Fig. 3.
Fig. 3. Representative eye diagrams at 25Gb/s cases (from left to right: best, intermediate, worst). Unit for the horizontal axis: 8 ps/div; unit for the vertical axis. 28.8, 20, 15.7 mV/div (left, middle, right).
Fig. 4.
Fig. 4. Representative S11 response. (Lowest: blue; intermediate: red; highest: yellow).
Fig. 5.
Fig. 5. The relations between the (a) BER, (b) ER, (c) RMS jitter and the arithmetic mean of the S11 response over three specific frequency ranges of 19 GHz, 25 GHz, 40 GHz.
Fig. 6.
Fig. 6. The correlation coefficients between the BER, SNR, ER, PP jitter, RMS jitter and the arithmetic mean of the S11 response over different frequency ranges.
Fig. 7.
Fig. 7. The correlation coefficients between the BER, SNR, ER, PP jitter, RMS jitter and the weighted mean of the S11 response over different frequency ranges.
Fig. 8.
Fig. 8. Junction capacitance variation for a p-i-n diode when the i-region width is subject to fabrication variation by an amount δWi. C0=Cpin(Wi) is the original p-i-n junction capacitance when δWi=0.

Tables (1)

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Table 1. Partial correlation coefficient p and correlation coefficient ρ

Equations (5)

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ρ ( y , x ) = i ( y i y ¯ ) ( x i x ¯ ) / i ( y i y ¯ ) 2 i ( x i x ¯ ) 2 ,
p ( y , x ; z ) [ ρ ( y , x ) ρ ( y , z ) ρ ( x , z ) ] / [ 1 ρ 2 ( y , z ) 1 ρ 2 ( x , z ) ]
P = P 0 + P 1 cos ( Δ ϕ Δ ϕ 0 ) ,
P = P 0 + P 1 cos ( g V b i V j Δ ϕ 0 ) ,
C p i n = C j 1 + ( W i / W p n ) 2 ,

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