Abstract

We investigated the dynamic response of a cascaded-ring-resonator-loaded Mach–Zehnder modulator (CRR-MZM), in which a number of cascaded ring resonators (RRs) are loaded in the interferometer as phase modulators. The analytical form is derived for the small-signal response of CRR-MZM using temporal-coupled-mode (TCM) theory, and its validity is confirmed by numerical calculations. It is revealed that the bandwidth of the CRR-MZM is maximized by setting proper delays in driving signals between neighboring RRs; the optimized delay is twice the photon lifetime of each RR. The calculated performances of CRR-MZMs are compared with those of standard modulators based on a single-ring-resonator (SRR) without interferometer, in terms of the modulation depth and bandwidth. For a given degree of the refractive index change in a waveguide, CRR-MZM can provide a larger modulation depth than a SRR-type modulator in frequency ranges exceeding 25 GHz.

© 2012 OSA

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2012 (2)

2011 (3)

2010 (5)

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (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]

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

P. Dong, S. Liao, H. Liang, W. Qian, X. Wang, R. Shafiiha, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “High-speed and compact silicon modulator based on a racetrack resonator with a 1 V drive voltage,” Opt. Lett. 35(19), 3246–3248 (2010).
[CrossRef] [PubMed]

2009 (1)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (2)

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

H. Tazawa, Y. Kuo, I. Dunayevskiy, J. Luo, A. K. Y. Jen, H. Fetterman, and W. Steier, “Ring resonator based electrooptic polymer traveling-wave modulator,” J. Lightwave Technol. 24(9), 3514–3519 (2006).
[CrossRef]

2004 (1)

2002 (2)

M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19(9), 2052–2059 (2002).
[CrossRef]

I. L. Gheorma and R. M. Osgood, “Fundamental limitations of optical resonator based on high-speed EO modulators,” IEEE Photon. Technol. Lett. 14(6), 795–797 (2002).
[CrossRef]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

1999 (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]

1987 (1)

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

Ahn, D.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Akiyama, S.

S. Akiyama, T. Kurahashi, K. Morito, T. Yamamoto, T. Usuki, and S. Nomura, “Cascaded-ring-resonator-loaded Mach-Zehnder modulator for enhanced modulation efficiency in wide optical bandwidth,” Opt. Express 20(15), 16321–16338 (2012).
[CrossRef]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

Apsel, A. B.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Asghari, M.

Baba, T.

H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011).
[CrossRef] [PubMed]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

Beals, M.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Beattie, J.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

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]

Bennett, B. R.

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

Brimont, A.

Cai, X.

Carothers, D.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Chen, Y. K.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

Chen, Y.-K.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[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]

Conway, T.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Cunningham, J. E.

Dong, P.

Dunayevskiy, I.

Fan, S.

Fedeli, J. M.

Fedeli, J.-M.

Feng, D.

Fetterman, H.

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]

Gardes, F. Y.

Gheorma, I. L.

I. L. Gheorma and R. M. Osgood, “Fundamental limitations of optical resonator based on high-speed EO modulators,” IEEE Photon. Technol. Lett. 14(6), 795–797 (2002).
[CrossRef]

Gill, D. M.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Grove, M.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Gutierrez, A. M.

Hatori, N.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

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]

Herrera, J.

Hill, C. M.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

Hong, C.-Y.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Ibanescu, M.

Ippen, E.

Ishikura, N.

Jen, A. K. Y.

Joannopoulos, J. D.

Johnson, S. G.

Kamocsai, R. L.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

Kimerling, L. C.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Krishnamoorthy, A. V.

Kuo, Y.

Kurahashi, T.

S. Akiyama, T. Kurahashi, K. Morito, T. Yamamoto, T. Usuki, and S. Nomura, “Cascaded-ring-resonator-loaded Mach-Zehnder modulator for enhanced modulation efficiency in wide optical bandwidth,” Opt. Express 20(15), 16321–16338 (2012).
[CrossRef]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[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]

Li, G.

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]

Liang, H.

Liao, S.

Lipson, M.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007).
[CrossRef] [PubMed]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

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, J.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Luo, J.

Luo, Y.

Manipatruni, S.

Marris-Morini, D.

Marti, J.

Martí, J.

Michel, J.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185 (2009).
[CrossRef]

Morito, K.

Nguyen, H. C.

Nomura, S.

Osgood, R. M.

I. L. Gheorma and R. M. Osgood, “Fundamental limitations of optical resonator based on high-speed EO modulators,” IEEE Photon. Technol. Lett. 14(6), 795–797 (2002).
[CrossRef]

Pan, D.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Patel, S. S.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Pomerene, A.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

Pomerene, A. T.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Poon, J. K. S.

Qian, W.

Raj, K.

Rasigade, G.

Rasras, M.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Reed, G. T.

Sacher, W. D.

Sakai, Y.

Sanchis, P.

Schmidt, B.

Schwelb, O.

Sekaric, L.

F. Xia, L. Sekaric, and Y. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Shafiiha, R.

Shakya, J.

Shinkawa, M.

Shubin, I.

Soljacic, M.

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]

Soref, R. A.

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

Sparacin, D. K.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Steier, W.

Taylor, H. F.

Tazawa, H.

Thacker, H.

Thomson, D. J.

Tu, K. Y.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

Tu, K.-Y.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Usuki, T.

S. Akiyama, T. Kurahashi, K. Morito, T. Yamamoto, T. Usuki, and S. Nomura, “Cascaded-ring-resonator-loaded Mach-Zehnder modulator for enhanced modulation efficiency in wide optical bandwidth,” Opt. Express 20(15), 16321–16338 (2012).
[CrossRef]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

Vivien, L.

Vlasov, Y. A.

F. Xia, L. Sekaric, and Y. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Wang, X.

White, A. E.

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (2010).
[CrossRef]

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

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]

Wong, C. W.

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Xia, F.

F. Xia, L. Sekaric, and Y. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Xu, Q.

Yamamoto, T.

S. Akiyama, T. Kurahashi, K. Morito, T. Yamamoto, T. Usuki, and S. Nomura, “Cascaded-ring-resonator-loaded Mach-Zehnder modulator for enhanced modulation efficiency in wide optical bandwidth,” Opt. Express 20(15), 16321–16338 (2012).
[CrossRef]

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

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.

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

Ye, T.

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.

Ziebell, M.

Appl. Phys. Express (1)

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “A 1V peak-to-peak driven 10-Gbps slow-light silicon Mach-Zehnder modulator using cascaded ring resonators,” Appl. Phys. Express 3(7), 072202 (2010).
[CrossRef]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

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

D. M. Gill, S. S. Patel, M. Rasras, K. Y. Tu, A. E. White, Y. K. Chen, A. Pomerene, D. Carothers, R. L. Kamocsai, C. M. Hill, and J. Beattie, “CMOS-compatible Si-ring-assisted Mach-Zehnder interferometer with internal bandwidth equalization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 45–52 (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]

IEEE Photon. Technol. Lett. (1)

I. L. Gheorma and R. M. Osgood, “Fundamental limitations of optical resonator based on high-speed EO modulators,” IEEE Photon. Technol. Lett. 14(6), 795–797 (2002).
[CrossRef]

J. Lightwave Technol. (6)

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

Nat. Photonics (1)

F. Xia, L. Sekaric, and Y. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Proc. IEEE (1)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185 (2009).
[CrossRef]

Proc. SPIE (1)

L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502, 612502-10 (2006).
[CrossRef]

Other (6)

H. Kaneshige, Y. Ueyama, H. Yamada, T. Arakawa, and Y. Kokubun, “Quantum well Mach-Zehnder modulator with single microring resonator and optimized arm length,” 17th Microoptics Conference (MOC' 11), Sendai, Japan, paper G-5, (2011).

J. Rosenberg, W. M. Green, A. Rylyakov, C. Schow, S. Assefa, B. G. Lee, C. Jahnes, and Y. Vlasov, “Ultra-low-voltage micro-ring modulator integrated with a CMOS feed-forward equalization driver,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWQ4 (2011).

W. D. Sacher, W. M. J. Green, S. Assefa, T. Barwicz, S. M. Shank, Y. A. Vlasov, and J. K. S. Poon, “Controlled coupling in silicon microrings for high-speed, high extinction ratio, and low-chirp modulation,” in Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference (CLEO/QELS 2011), paper PDPA8 (2011).

J. C. Rosenberg, W. M. J. Green, S. Assefa, T. Barwicz, M. Yang, S. M. Shank, and Y. A. Vlasov, “Low-power 30 Gbps silicon microring modulator,” in Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference (CLEO/QELS 2011), paper PDPB9 (2011).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, second edition, (Princeton University Press, 2008).

K. Okamoto, Fundamentals of Optical Waveguides, (Academic Press, 2006), Chap. 5.

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Figures (8)

Fig. 1
Fig. 1

Schematic view of RR-based modulators in two different configurations, and definition of parameters used in this paper. (a) SRR-SSM. (b) Coupling between ring and bus waveguide as a part of RRs. y2 and 1 − y2 indicate the fraction of the power transmitted to the bus and the ring waveguide, respectively. (c) CRR-MZM. d indicates the time delay set in the electrical signals between two neighboring RRs.

Fig. 2
Fig. 2

Schematic structure of phase modulator based on CRRs (top) and calculation diagram for small signal responses (bottom). In each RR, three frequency components of light are created in small signal analysis. One is the input light with angular frequency ω, and the others are with ω ± Ω, which are side-bands that were created around ω due to the modulation. aj(0) and aj ± are the amplitude of those frequency components. The bold arrows indicate the dependencies of these three frequency components on those at the previous RR at the first (black) and j-th RR (red), respectively.

Fig. 3
Fig. 3

Calculated small-signal response of SRR-SSM (black) and CRR-MZMs with single (green) or 10 RRs (blue and red) on each arm. The modulation frequency is normalized by the photon lifetime of RR. For one of the 10 CRR-MZMs (blue), modulation signals are applied to the RRs with the same timing, whereas a delay of d = 2τ is set in signals between neighboring RRs for the other (red).

Fig. 4
Fig. 4

Configuration and definition of variables used in numerical calculations to obtain the response of a single RR.

Fig. 5
Fig. 5

Comparison of calculated responses of CRR-MZM with N = 5, between analytical (narrow) and numerical (bold) methods, for relatively small-coupling high-Q RR with 1-y2 = 5% (red) and large-coupling low-Q RR with 1-y2 = 40% (blue).

Fig. 6
Fig. 6

(a) Calculated DC response (solid) and 3-dB bandwidth (dashed) of SRR-SSM (black) and CRR-MZM (red, green, and blue) for an RR photon lifetime of 0.2-200 ps. No propagation loss is assigned to the waveguide for CRR-MZMs, whereas loss that causes critical coupling is assigned to SRR-SSM. (b) Parametric plot between DC response and 3-dB bandwidth using photon lifetime as the parameter.

Fig. 7
Fig. 7

(a) Calculated DC response (solid) and 3-dB bandwidth (dashed) of SRR-SSM (black) and CRR-MZM (red, green, and blue), for photon lifetime of RR of 0.2-200 ps. A propagation loss of αdB = 10 dB/cm is assigned to the waveguide for CRR-MZMs, whereas loss cause critical coupling is assigned to SRR-SSM. (b) Parametric plot between DC response and 3-dB bandwidth using photon lifetime as parameter.

Fig. 8
Fig. 8

Calculated outputs as eye diagrams for 50-Gb/s PRBS signal of 27-1. (a) SRR-SSM (b) CRR-MZM with N = 4 (b).

Tables (1)

Tables Icon

Table 1 Conditions of numerical calculations

Equations (23)

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dA( t ) dt =( i ω r ( t ) 1 τ c 1 τ l )A( t )+ 2 τ c S in ( t ).
S out ( t )= S in ( t )+ 2 τ c A( t ).
1 τ c = ( 1 y 2 ) v g 2( 2πR ) ,and
1 τ l = α dB v g 20 log 10 e .
ω r ( t )= ω 0 + δ ω cos{ Ω( td ) },
da( t ) dt =[ i{ Δ ω + δ ω cosΩ( td ) } 1 τ ]a( t )+μ S 0 ,whereμ= 2 τ c .
1 τ = 1 τ c + 1 τ l .
a( t )= e b( t ) 0 t e b( x ) μ S 0 dx ,
whereb( x )= 0 x [ i Δ ω +i δ ω cos{ Ω( td ) } 1 τ ]dt =( i Δ ω 1 τ )x+i δ ω Ω [ sin{ Ω( xd ) }+sin( Ωd ) ].
e i δ ω Ω [ sin{ Ω( td ) }+sin( Ωd ) ] 1 i δ ω Ω [ sin{ Ω( td ) }+sin( Ωd ) ].
S out e iωt S 0 =( 1+ μ 2 τ h )+ δ ω τ μ 2 τ 2Ωτ ( 1 h 1 h+iΩτ ) e iΩ( td ) + δ ω τ μ 2 τ 2Ωτ ( 1 hiΩτ 1 h ) e iΩ( td ) = F (0) ( μ 2 τ, Δ ω τ )+ δ ω τ F + ( μ 2 τ, Δ ω τ,Ωτ ) e iΩ( td ) + δ ω τ F ( μ 2 τ, Δ ω τ,Ωτ ) e iΩ( td ) ,
| S out | 2 = 1 2 + δ ω τ ( Ωτ ) 2 +1 ( Ωτ ) 4 +4 sin{ Ω( td )+ φ 0 }.
a j ± = F (0) ( μ 2 τ,Ωτ ) a j1 ± + δ ω τ F ± ( μ 2 τ,0,Ωτ ) e iΩ( j1 )d a j1 (0) ,and
a j (0) = F (0) ( μ 2 τ,0 ) a j1 (0) ,
a N ± = δ ω τ F ± ( μ 2 τ,0,Ωτ ) j=1 N [ e iΩ( Nj )d { F (0) ( μ 2 τ,0 ) } Nj { F (0) ( μ 2 τ,Ωτ ) } j1 ] .
a N (0) = { F (0) ( μ 2 τ,0 ) } N .
S out e iωt = 1 2 [ α N + e iΩt + α N (0) + α N e iΩt ]+ i 2 [ α N + e iΩt + α N (0) α N e iΩt ].
| S out | 2 = 1 2 + δ ω τ 2 1+ ( Ωτ ) 2 | j=1 N e i( Ωd2θ )j |sin{ Ωt+ φ ( Ω ) },wheretanθ=Ωτ,
1 v g u t + u z =0.
u 1 ( t )=y u 2 ( t ) e α( 2πR )+iφ( t ) i 1 y 2 u 0 ( t ).
u 3 ( t )=y u 0 ( t )i 1 y 2 u 2 ( t ) e α( 2πR )+iφ( t ) .
u 2 ( t m )= u 1 ( t m1 ).
φ( t )= Δ ω + δ ω cos[ Ω{ t( j1 )d } ] f FSR ,

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