Abstract

We present an accurate behavior model for Si micro-ring modulators (MRM) based on Verilog-A, a standard simulation tool for electronic system design. Our model describes the electrical characteristics of the Si MRM using an equivalent circuit and the optical characteristics based on the couple-mode theory. The accuracy of our model is confirmed by comparing simulation results of our behavior model with the measurement results of a fabricated Si MRM. With this behavior model, co-simulation of Si MRM and electronic driving circuits in the standard electronic design environment can be easily performed.

© 2015 Optical Society of America

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References

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    [Crossref]
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  7. J.-S. Youn, M.-J. Lee, K.-Y. Park, H. Rücker, and W.-Y. Choi, “An integrated 12.5-Gb/s optoelectronic receiver with a silicon avalanche photodetector in standard SiGe BiCMOS technology,” Opt. Express 20(27), 28153–28162 (2012).
    [Crossref] [PubMed]
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    [Crossref]
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  11. K. Zhu, V. Saxena, and W. Kuang, “Compact Verilog-A modeling of silicon traveling-wave modulator for hybrid CMOS photonic circuit design,” in Proceedings of IEEE International Midwest Symposium on Circuits and Systems, pp. 615–618 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
  15. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [Crossref]
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    [Crossref]
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  18. X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
    [Crossref] [PubMed]
  19. W. D. Sacher, W. M. J. Green, S. Assefa, T. Barwicz, H. Pan, S. M. Shank, Y. A. Vlasov, and J. K. S. Poon, “Coupling modulation of microrings at rates beyond the linewidth limit,” Opt. Express 21(8), 9722–9733 (2013).
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  20. J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
    [Crossref] [PubMed]
  21. Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
    [Crossref]

2014 (3)

W. Bogaerts, M. Fiers, and P. Dumon, “Design challenges in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202008 (2014).
[Crossref]

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (6)

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

M. A. Taubenblatt, “Optical interconnects for high-performance computing,” IEEE/OSA J. Lightwave Technol. 30(4), 448–457 (2012).
[Crossref]

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

J.-S. Youn, M.-J. Lee, K.-Y. Park, H. Rücker, and W.-Y. Choi, “An integrated 12.5-Gb/s optoelectronic receiver with a silicon avalanche photodetector in standard SiGe BiCMOS technology,” Opt. Express 20(27), 28153–28162 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (2)

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Alic, N.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Alon, E.

Amberg, P.

Asghari, M.

Assefa, S.

Azadeh, S. S.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Ban, Y.

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

Barwicz, T.

Beausoleil, R. G.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Block, B. A.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Bogaerts, W.

W. Bogaerts, M. Fiers, and P. Dumon, “Design challenges in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202008 (2014).
[Crossref]

Buckwalter, J. F.

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

Chang, P. L. D.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Chi, H.-K.

Cho, M. H.

Cho, S.-H.

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

Choi, W.-Y.

J.-S. Youn, M.-J. Lee, K.-Y. Park, H. Rücker, and W.-Y. Choi, “An integrated 12.5-Gb/s optoelectronic receiver with a silicon avalanche photodetector in standard SiGe BiCMOS technology,” Opt. Express 20(27), 28153–28162 (2012).
[Crossref] [PubMed]

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

Chrostowski, L.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Cone, C.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Cunningham, J. E.

Dayringer, M.

Dong, P.

Dumon, P.

W. Bogaerts, M. Fiers, and P. Dumon, “Design challenges in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202008 (2014).
[Crossref]

Fedeli, J.-M.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Feng, D.

Ferguson, J.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Fiers, M.

W. Bogaerts, M. Fiers, and P. Dumon, “Design challenges in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202008 (2014).
[Crossref]

Flueckiger, J.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Gainsley, J.

García, S. R.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Gardes, F. Y.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Goll, B.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Green, W. M. J.

Gunupudi, P.

Hauck, J.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Ho, R.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Hochberg, M.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Hu, Y.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Hwang, M.-S.

Jang, K.-S.

Jeong, D.-K.

Joo, J.

Kern, A. M.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Kim, D.-W.

Kim, G.

Kim, H.-C.

Kim, I. G.

Kim, J. H.

Kim, J.-K.

Kim, S.

Kim, S. A.

Klein, J.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Knoll, D.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Krishnamoorthy, A. V.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Kuang, W.

K. Zhu, V. Saxena, and W. Kuang, “Compact Verilog-A modeling of silicon traveling-wave modulator for hybrid CMOS photonic circuit design,” in Proceedings of IEEE International Midwest Symposium on Circuits and Systems, pp. 615–618 (2014).
[Crossref]

Kuo, B. P. P.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Lee, J. M.

Lee, J. Y.

Lee, J.-M.

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

Lee, M.-J.

Lexau, J.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Li, G.

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Li, J.

Li, Y.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Liao, J. T. S.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Lin, C.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Lischke, S.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Liu, F.

Liu, F. Y.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

Luo, Y.

Mashanovich, G. Z.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Mcgarry, S.

Mekis, A.

Merget, F.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Moghadam, H. F.

Mohammed, E.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Müller, J.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Myslivets, E.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Oh, J. H.

Palermo, S.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Pan, H.

Park, G. S.

Park, J. M.

Park, J. W.

Park, K.-S.

Park, K.-Y.

Patil, D.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Pinguet, T.

Pond, J.

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Poon, J. K. S.

Porte, H.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Radic, S.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Raj, K.

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Reed, G. T.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Reshotko, M. R.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Rhim, J.

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

Rücker, H.

Sacher, W. D.

Saxena, V.

K. Zhu, V. Saxena, and W. Kuang, “Compact Verilog-A modeling of silicon traveling-wave modulator for hybrid CMOS photonic circuit design,” in Proceedings of IEEE International Midwest Symposium on Circuits and Systems, pp. 615–618 (2014).
[Crossref]

Shank, S. M.

Shen, B.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Shubin, I.

Smy, T.

Song, M.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Taubenblatt, M. A.

M. A. Taubenblatt, “Optical interconnects for high-performance computing,” IEEE/OSA J. Lightwave Technol. 30(4), 448–457 (2012).
[Crossref]

Thacker, H.

Thacker, H. D.

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

Thomson, D. J.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Vlasov, Y. A.

Willner, A. E.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Witzens, J.

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Yang, J.-Y.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Yao, J.

Ye, W. N.

Youn, J.-S.

Young, I. A.

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

Yu, B.-M.

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

Zhang, L.

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

Zheng, X.

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Zhu, K.

K. Zhu, V. Saxena, and W. Kuang, “Compact Verilog-A modeling of silicon traveling-wave modulator for hybrid CMOS photonic circuit design,” in Proceedings of IEEE International Midwest Symposium on Circuits and Systems, pp. 615–618 (2014).
[Crossref]

Zimmermann, H.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Zimmermann, L.

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

Zlatanovic, S.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

W. Bogaerts, M. Fiers, and P. Dumon, “Design challenges in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202008 (2014).
[Crossref]

L. Zhang, Y. Li, J.-Y. Yang, M. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010).
[Crossref]

IEEE J. Solid-State Circuits (2)

I. A. Young, E. Mohammed, J. T. S. Liao, A. M. Kern, S. Palermo, B. A. Block, M. R. Reshotko, and P. L. D. Chang, “Optical I/O technology for tera-scale computing,” IEEE J. Solid-State Circuits 45(1), 235–248 (2010).
[Crossref]

J. F. Buckwalter, X. Zheng, G. Li, K. Raj, and A. V. Krishnamoorthy, “A monolithic 25-Gb/s transceiver with photonic ring modulators and Ge detectors in a 130-nm CMOS SOI process,” IEEE J. Solid-State Circuits 47(6), 1309–1322 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (1)

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

IEEE/OSA J. Lightwave Technol. (2)

X. Zheng, F. Y. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. D. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow power 80 Gb/s arrayed CMOS silicon photonic transceivers for WDM optical links,” IEEE/OSA J. Lightwave Technol. 30(4), 641–650 (2012).
[Crossref]

M. A. Taubenblatt, “Optical interconnects for high-performance computing,” IEEE/OSA J. Lightwave Technol. 30(4), 448–457 (2012).
[Crossref]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (5)

G. Kim, J. W. Park, I. G. Kim, S. Kim, S. Kim, J. M. Lee, G. S. Park, J. Joo, K.-S. Jang, J. H. Oh, S. A. Kim, J. H. Kim, J. Y. Lee, J. M. Park, D.-W. Kim, D.-K. Jeong, M.-S. Hwang, J.-K. Kim, K.-S. Park, H.-K. Chi, H.-C. Kim, D.-W. Kim, and M. H. Cho, “Low-voltage high-performance silicon photonic devices and photonic integrated circuits operating up to 30 Gb/s,” Opt. Express 19(27), 26936–26947 (2011).
[Crossref] [PubMed]

X. Zheng, Y. Luo, G. Li, I. Shubin, H. Thacker, J. Yao, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators,” Opt. Express 20(10), 11478–11486 (2012).
[Crossref] [PubMed]

J.-S. Youn, M.-J. Lee, K.-Y. Park, H. Rücker, and W.-Y. Choi, “An integrated 12.5-Gb/s optoelectronic receiver with a silicon avalanche photodetector in standard SiGe BiCMOS technology,” Opt. Express 20(27), 28153–28162 (2012).
[Crossref] [PubMed]

W. D. Sacher, W. M. J. Green, S. Assefa, T. Barwicz, H. Pan, S. M. Shank, Y. A. Vlasov, and J. K. S. Poon, “Coupling modulation of microrings at rates beyond the linewidth limit,” Opt. Express 21(8), 9722–9733 (2013).
[Crossref] [PubMed]

X. Zheng, D. Patil, J. Lexau, F. Liu, G. Li, H. Thacker, Y. Luo, I. Shubin, J. Li, J. Yao, P. Dong, D. Feng, M. Asghari, T. Pinguet, A. Mekis, P. Amberg, M. Dayringer, J. Gainsley, H. F. Moghadam, E. Alon, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-efficient 10 Gb/s hybrid integrated silicon photonic transmitter and receiver,” Opt. Express 19(6), 5172–5186 (2011).
[Crossref] [PubMed]

Proc. SPIE (1)

L. Chrostowski, J. Flueckiger, C. Lin, M. Hochberg, J. Pond, J. Klein, J. Ferguson, and C. Cone, “Design methodologies for silicon photonic integrated circuits,” Proc. SPIE 8989, 89890G (2014).

Sci. Rep. (1)

J. Müller, F. Merget, S. S. Azadeh, J. Hauck, S. R. García, B. Shen, and J. Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
[Crossref] [PubMed]

Other (5)

Y. Ban, J.-M. Lee, B.-M. Yu, S.-H. Cho, and W.-Y. Choi, “Small-signal frequency responses for Si micro-ring modulators,” in Proceedings of IEEE Optical Interconnects Conference, pp. 47–48 (2014).
[Crossref]

L. Zimmermann, D. J. Thomson, B. Goll, D. Knoll, S. Lischke, F. Y. Gardes, Y. Hu, G. T. Reed, H. Zimmermann, and H. Porte, “Monolithically integrated 10Gbit/sec Silicon modulator with driver in 0.25μm SiGe:C BiCMOS,” in Proceedings of European Conference on Optical Communication (ECOC), pp. 1–3 (2013).

K. Zhu, V. Saxena, and W. Kuang, “Compact Verilog-A modeling of silicon traveling-wave modulator for hybrid CMOS photonic circuit design,” in Proceedings of IEEE International Midwest Symposium on Circuits and Systems, pp. 615–618 (2014).
[Crossref]

J. Rhim, Y. Ban, J.-M. Lee, S.-H. Cho, and W.-Y. Choi, “A behavior model for silicon micro-ring modulators and transmitter circuit-level simulation using it,” in Proceedings of IEEE International Conference on Group IV Photonics, pp. 7–8 (2014).
[Crossref]

B.-M. Yu, J.-M. Lee, Y. Ban, S.-H. Cho, and W.-Y. Choi, “Model parameter extraction for Si micro-ring modulators,” presented at OptoElectronics and Communication Conference and the Australian Conference on Optical Fibre Technology (OECC/ACOFT), Melbourne, Australia, 6–10 July, 2014.

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Figures (11)

Fig. 1
Fig. 1 Structure of Si MRM.
Fig. 2
Fig. 2 Equivalent circuit model for Si MRM.
Fig. 3
Fig. 3 Step change in the modulation voltage and numerical calculation of a(t).
Fig. 4
Fig. 4 Behavioral model in Verilog-A.
Fig. 5
Fig. 5 (a) Microphotograph and (b) cross-section of fabricated Si MRM.
Fig. 6
Fig. 6 Curve-fitting of the simulated S11 to the measurements: (a) Magnitude response (b) Phase response.
Fig. 7
Fig. 7 (a) Measured and fitted optical transmission characteristics. (b) Extracted ηeff / m. (c) Extracted τl and τe.
Fig. 8
Fig. 8 (a) Simulation setup. (b) Measurement setup.
Fig. 9
Fig. 9 Measured and simulated step response at the wavelength of (a) 1551.45 nm (b) 1551.50 nm (c) 1551.55 nm.
Fig. 10
Fig. 10 Measured and simulated frequency response at the wavelength of 1551.45 nm, 1551.50 nm, and 1551.55 nm.
Fig. 11
Fig. 11 Measured and simulated eye-diagrams for 28-Gb/s PRBS 231-1 pattern at the wavelength of (a) 1551.45 nm (b) 1551.50 nm (c) 1551.55 nm.

Tables (1)

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Table 1 Extracted parameter values of the Si MRM

Equations (12)

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d dt a(t)=( j ω r 1 τ )a(t)jμ E i (t).
E t (t)= E i (t)jμa(t).
a(t)=Pexp( j ω r t 1 τ t )+Qexp( jωt ),
v(t){ v 0 =v( t 0 ), t 0 t< t 1 v 1 =v( t 1 ), t 1 t< t 2 v k =v( t k ), t k t< t k+1 .
a(t)={ a 0 (t)= P 0 exp( j ω r,0 t 1 τ 0 t )+ Q 0 exp( jωt ), t 0 t< t 1 a 1 (t)= P 1 exp( j ω r,1 t 1 τ 1 t )+ Q 1 exp( jωt ), t 1 t< t 2 a k (t)= P k exp( j ω r,k t 1 τ k t )+ Q k exp( jωt ), t k t< t k+1 ,
Q 0 = j 2 τ e,0 j( ω ω r,0 )+ 1 τ 0 E 0 .
P 1 =[ a 0 ( t 1 ) Q 1 exp( jω t 1 ) ]exp( j ω r,1 t 1 + 1 τ 1 t 1 ),
P k =[ a k1 ( t k ) Q k exp( jω t k ) ]exp( j ω r,k t k + 1 τ k t k ).
Q k = j 2 τ e,k j( ω ω r,k )+ 1 τ k E 0 .
a k (t)= P k exp( j ω r,k t 1 τ k t )+ Q k exp( jωt ) =[ a k1 ( t k ) Q k exp( jω t k ) ]exp[ ( j ω r,k 1 τ k )( t t k ) ]+ Q k exp( jωt ).
A k = a k ( t k )= a k1 ( t k ) =[ a k2 ( t k1 ) Q k1 exp( jω t k1 ) ]exp[ ( j ω r,k1 1 τ k1 )Δt ]+ Q k1 exp( jω t k ) =[ A k1 Q k1 exp( jω t k1 ) ]exp[ ( j ω r,k1 1 τ k1 )Δt ]+ Q k1 exp( jω t k ).
| E t E i | 2 = | j( ω ω r )+ 1 τ l 1 τ e j( ω ω r )+ 1 τ l + 1 τ e | 2 .

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