Abstract

An analytic model is developed to study the dynamic response of carrier-depletion silicon ring modulators. Its validity is confirmed by a detailed comparison between the modeled and the measured small signal frequency response of a practical device. The model is used to investigate how to maximize the optical modulation amplitude (OMA) and how the OMA could be traded for the bandwidth by tuning the coupling strength and the operation wavelength. Our calculation shows that for a ring modulator with equal RC time constant and photon lifetime, if its operation wavelength shifts from the position of the maximum OMA towards the direction that is away from the resonance, the 3dB modulation bandwidth increases ~2.1 times with a penalty of 3 dB to the OMA.

© 2014 Optical Society of America

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References

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2013 (4)

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

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]

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

T. Baba, S. Akiyama, M. Imai, N. Hirayama, H. Takahashi, Y. Noguchi, T. Horikawa, and T. Usuki, “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21(10), 11869–11876 (2013).
[Crossref] [PubMed]

2012 (6)

2011 (2)

2010 (4)

2009 (2)

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
[Crossref] [PubMed]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

2008 (1)

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]

Absil, P.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Akiyama, S.

Asghari, M.

Assefa, S.

Ayazi, A.

Baba, T.

Baehr-Jones, T.

Baets, R.

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

Barwicz, T.

Beausoleil, R. G.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Biberman, A.

Bogaerts, W.

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Cai, X.

Christie, P.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

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]

Chu, T.

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

Cunningham, J. E.

Ding, R.

Dong, P.

Dwivedi, S.

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

Fedeli, J. M.

Feng, D.

Feng, N. N.

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]

Fournier, M.

Gill, D. M.

Goossens, D.

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Gould, M.

Green, W. M. J.

Guha, B.

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]

Hirayama, N.

Hochberg, M.

Horikawa, T.

Hu, Y.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

Huang, S.

Imai, M.

Jen, A. K. Y.

Krishnamoorthy, A. V.

Kung, C. C.

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]

Lepage, G.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Li, G.

Li, X.

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

Li, Y.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Li, Z.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

Liang, H.

Liao, S.

Lim, A. E.

Lipson, M.

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, Y.

Luo, J.

Luo, Y.

Masood, A.

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Noguchi, Y.

Pan, H.

Pantouvaki, M.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Poon, J. K.

Poon, J. K. S.

Preston, K.

Qian, W.

Raj, K.

Rakowski, M.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

Rosenberg, J. C.

Sacher, W. D.

Shafiiha, R.

Shank, S. M.

Shubin, I.

Song, M.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Takahashi, H.

Thacker, H.

Timurdogan, E.

Trotter, D. C.

Usuki, T.

Van Campenhout, J.

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

Van Hoovels, N.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

Van Thourhout, D.

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Verheyen, P.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

Vlasov, Y. A.

Wang, X.

Watts, M. R.

Willner, A. E.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Xiao, X.

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

Xiong, K.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

Xu, H.

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

Yang, J.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Yang, M.

Yao, J.

Ye, T.

Yu, H.

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

Yu, J.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

Yu, Y.

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

Zhang, L.

L. Zhang, Y. Li, J. 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]

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

Zheng, D.

Zheng, X.

Zortman, W. A.

Appl. Phys., A Mater. Sci. Process. (1)

L. Zhang, Y. Li, M. Song, J. Yang, R. G. Beausoleil, and A. E. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys., A Mater. Sci. Process. 95(4), 1089–1100 (2009).
[Crossref]

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

M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. Van Hoovels, P. Absil, and J. Van Campenhout, “Comparison of silicon ring modulators with interdigitated and lateral PN junctions,” IEEE J. Sel. Top. Quantum Electron. 19(2), 7900308 (2013).
[Crossref]

L. Zhang, Y. Li, J. 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 Photon. Technol. Lett. (2)

X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, “44-Gb/s silicon microring modulators based on zigzag PN junctions,” IEEE Photon. Technol. Lett. 24(19), 1712–1714 (2012).
[Crossref]

H. Yu, M. Pantouvaki, S. Dwivedi, P. Verheyen, G. Lepage, R. Baets, W. Bogaerts, and J. Van Campenhout, “Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide,” IEEE Photon. Technol. Lett. 25(2), 159–162 (2013).
[Crossref]

J. Lightwave Technol. (2)

T. Ye and X. Cai, “On power consumption of silicon-microring-based optical modulators,” J. Lightwave Technol. 28(11), 1615–1623 (2010).
[Crossref]

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]

Opt. Express (11)

W. D. Sacher and J. K. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16(20), 15741–15753 (2008).
[Crossref] [PubMed]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N. N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18(11), 10941–10946 (2010).
[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]

G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Express 19(21), 20435–20443 (2011).
[Crossref] [PubMed]

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012).
[Crossref] [PubMed]

J. C. Rosenberg, W. M. J. Green, S. Assefa, D. M. Gill, T. Barwicz, M. Yang, S. M. Shank, and Y. A. Vlasov, “A 25 Gbps silicon microring modulator based on an interleaved junction,” Opt. Express 20(24), 26411–26423 (2012).
[Crossref] [PubMed]

A. Biberman, E. Timurdogan, W. A. Zortman, D. C. Trotter, and M. R. Watts, “Adiabatic microring modulators,” Opt. Express 20(28), 29223–29236 (2012).
[Crossref] [PubMed]

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
[Crossref] [PubMed]

T. Baba, S. Akiyama, M. Imai, N. Hirayama, H. Takahashi, Y. Noguchi, T. Horikawa, and T. Usuki, “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21(10), 11869–11876 (2013).
[Crossref] [PubMed]

M. Gould, T. Baehr-Jones, R. Ding, S. Huang, J. Luo, A. K. Y. Jen, J. M. Fedeli, M. Fournier, and M. Hochberg, “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Express 19(5), 3952–3961 (2011).
[Crossref] [PubMed]

A. Ayazi, T. Baehr-Jones, Y. Liu, A. E. Lim, and M. Hochberg, “Linearity of silicon ring modulators for analog optical links,” Opt. Express 20(12), 13115–13122 (2012).
[Crossref] [PubMed]

Opt. Lett. (2)

Other (3)

G. Ghione, Semiconductor Devices for High-speed Optoelectronics (Cambridge, 2009), Chap. 6.

A. Masood, M. Pantouvaki, D. Goossens, G. Lepage, P. Verheyen, D. Van Thourhout, P. Absil, and W. Bogaerts, “CMOS-compatible tungsten heaters for silicon photonic waveguides,” Proc. 9th IEEE International Conference on Group IV Photonics, 234–236 (2012).
[Crossref]

J. Van Campenhout, M. Pantouvaki, P. Verheyen, S. Selvaraja, G. Lepage, H. Yu, W. Lee, J. Wouters, D. Goossens, M. Moelants, W. Bogaerts, and P. Absil, “Low-voltage, Low-loss, Multi-Gb/s silicon micro-ring modulator based on a MOS capacitor,” Proc. Optical Fiber Communication Conference, OM2E.4 (2012).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram of a typical carrier-depletion ring modulator with an integrated heater. (b) Cross-section of the rib waveguide. (c) Equivalent circuit of the device.
Fig. 2
Fig. 2 (a) Transmitted spectra of the ring modulator at different bias voltages. The discrete data points present the measurement result. The black dashed lines are the fitted curves. (b) The S11 parameter of the ring modulator with 0 V bias voltage. The solid and the dashed lines are the measured and the fitted curves, respectively. (c) Extinction ratio and insertion loss for a voltage swing from −0.5 V to 0.5 V.
Fig. 3
Fig. 3 (a) 3 dB bandwidths of the modeled OMA2 and the measured |S21|2 versus the operation wavelength. The inset presents the experiment setup diagram for the S21 parameter measurement. (b) Penalties to the modeled OMA (ΔOMA) and the measured |S21| at a low modulation frequency of 300 MHz as a function of the operation wavelength. The reverse bias voltage for the two figures is 0 V. Δλ is the wavelength offset from the resonance wavelength.
Fig. 4
Fig. 4 Frequency responses of the modeled OMA2 and the measured |S21|2 at different wavelengths. Both OMA2 and |S21|2 are normalized to their values at 300 MHz. The marked values inside the figures are the 3 dB cutoff frequency of OMA2 and |S21|2.
Fig. 5
Fig. 5 f3dB/fQ as a function of fRC/fQ for different coupling conditions. The device works at the optimum wavelength of λ = λ0 ± λFWHM/2/31/2 during the modeling.
Fig. 6
Fig. 6 (a) f3dB/fQ_l and ΔOMA as a function of τe/τl for different RC constants. (b) the relationships between f3dB/fQ_l and ΔOMA for different RC constants. The device works at the optimum wavelength which is calculated as λ0-λFWHM/2/31/2. The penalty to OMA is induced by reducing τe (increasing the coupling between the ring and the bus waveguide) from τe/τl≈1.7.
Fig. 7
Fig. 7 (a) f3dB/fQ and ΔOMA as a function of (λ-λ0) /λFWHM for different RC constants. (b) The relationships between f3dB/fQ and ΔOMA for different RC constants. The device works at the coupling condition of τe = 2τl. The penalty to OMA is induced by reducing the wavelength from (λ-λ0) /λFWHM = −0.32.

Tables (1)

Tables Icon

Table 1 Parameters of resonance curves at different bias voltages

Equations (15)

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v pn ( ω 1 )= v 0 f( ω 1 )cos[ ω 1 t+ϕ( ω 1 )]
f( ω 1 )=| Z DUT Z DUT +50 1 1+j ω 1 R 1 C 1 |
ϕ( ω 1 )=arg( Z DUT Z DUT +50 1 1+j ω 1 R 1 C 1 )
Z DUT = 1 j ω 1 C 0 ( 1 j ω 1 C 1 + R 1 ) ( 1 j ω 1 C 2 + R 2 )
d dt α(t)=(j ω 0 1 τ )α(t)jμA e jωt
S t (t)=Aexp(jωt)jμa(t)
S t =A j(ω ω 0 )+ 1 τ 2 τ e j(ω ω 0 )+ 1 τ exp(jωt)
ω 0 = ω 0 + Δ ω 0 Δ v pn v pn ( ω 1 )
( 1 τ ) = 1 τ + Δ( 1 τ ) Δ v pn v pn ( ω 1 )
d dt α(t)={ (j ω 0 1 τ )+j v 0 K pn f( ω 1 )cos[ ω 1 t+ϕ( ω 1 )] }α(t)jμA e jωt
α(t)=jμAexp{ (j ω 0 1 τ )t+j v 0 K pn f( ω 1 ) ω 1 sin[ ω 1 t+ϕ( ω 1 )] } × exp{ j(ω ω 0 )t+ t τ j v 0 K pn f( ω 1 ) ω 1 sin[ ω 1 t+ϕ( ω 1 )] }dt
α(t)=jμAexp[(j ω 0 1 τ )t] n= + J n [ v 0 K pn f( ω 1 ) ω 1 ]exp[jn( ω 1 t+ϕ( ω 1 )] × m= + J m [ v 0 K pn f( ω 1 ) ω 1 ] exp[j(ω ω 0 +m ω 1 )t+ t τ +jmϕ( ω 1 )] j(ω ω 0 +m ω 1 )+ 1 τ
S t (t)=Aexp(jωt){ j(ω ω 0 )+ 1 τ 2 τ e j(ω ω 0 )+ 1 τ j v 0 μ 2 K pn f( ω 1 ) [j(ω ω 0 )+ 1 τ ] 2 + ω 1 2 cos ω 1 t j v 0 μ 2 K pn f( ω 1 ) [j(ω ω 0 )+ 1 τ ] 2 + ω 1 2 ω 1 sin ω 1 t [j(ω ω 0 )+ 1 τ ] }
OMA| ω 1 <<1/τ =| 4Re{ j v 0 A 2 μ 2 [ Δ ω 0 Δ v pn j Δ( 1 τ ) Δ v pn ]f( ω 1 ) × ( 1 τ 2 τ e ) 1 τ (ω ω 0 ) 2 +j(ω ω 0 )( 2 τ 2 τ e ) [ (ω ω 0 ) 2 + 1 τ 2 ] 2 } |
OMA| ω 1 <<1/τ =| 4 v 0 A 2 μ 2 f( ω 1 ) Δ ω 0 Δ v pn (ω ω 0 )( 2 τ 2 τ e ) [ (ω ω 0 ) 2 + 1 τ 2 ] 2 |

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