Abstract

High speed coupling-modulation of a microring-based light drop structure is proposed, which removes severe signal distortion due to intracavity energy depletion and separates the modulation speed from the resonator linewidth restriction. Extinction ratio improvement from <1 dB to >20 dB with 40 Gb/s non-return-to-zero (NRZ) signals is obtained with 25 times smaller drive voltage. The tolerance to active ring propagation loss is increased from 5 dB/cm to over 25 dB/cm with less than 5% modulation bandwidth reduction. The possibility of obtaining 160 Gb/s NRZ signal with no more than 4 V drive voltage and less than 5 dB insertion loss is highlighted.

© 2012 OSA

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2012 (1)

2011 (1)

2010 (4)

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

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear Distortion in a Silicon Microring-Based Electro-Optic Modulator for Analog Optical Links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (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]

2009 (5)

2008 (2)

Y. Li, L. Zhang, M. Song, B. Zhang, J.-Y. Yang, R. G. Beausoleil, A. E. Willner, and P. D. Dapkus, “Coupled-ring-resonator-based silicon modulator for enhanced performance,” Opt. Express 16(17), 13342–13348 (2008).
[CrossRef] [PubMed]

V. M. N. Passaro and F. Dell’Olio, “Scaling and optimization of MOS optical modulators in nanometer SOI waveguides,” IEEE Trans. NanoTechnol. 7(4), 401–408 (2008).
[CrossRef]

2007 (3)

2005 (4)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[CrossRef]

2002 (1)

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[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]

Adibi, A.

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a silicon-on- insulator platform,” Opt. Express 17(4), 2247–2254 (2009).
[CrossRef] [PubMed]

Ansheng, L.

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[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.

Brimont, A.

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]

Chen, E.

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]

Choi, S. J.

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[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]

Dapkus, P. D.

Y. Li, L. Zhang, M. Song, B. Zhang, J.-Y. Yang, R. G. Beausoleil, A. E. Willner, and P. D. Dapkus, “Coupled-ring-resonator-based silicon modulator for enhanced performance,” Opt. Express 16(17), 13342–13348 (2008).
[CrossRef] [PubMed]

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

Dell’Olio, F.

V. M. N. Passaro and F. Dell’Olio, “Scaling and optimization of MOS optical modulators in nanometer SOI waveguides,” IEEE Trans. NanoTechnol. 7(4), 401–408 (2008).
[CrossRef]

Djordjev, K.

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

Fedeli, J.-M.

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]

Franck, T.

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]

Green, W. M. J.

Guo, J.

Gutierrez, A. M.

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]

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]

Hodge, D.

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]

Keil, U.

Koch, T. L.

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, C.

Li, J.

Li, Q.

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a silicon-on- insulator platform,” Opt. Express 17(4), 2247–2254 (2009).
[CrossRef] [PubMed]

Li, Y.

Liao, L.

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[CrossRef]

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

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, A.

Marris-Morini, D.

Marti, J.

Miller, D.

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

Morse, M.

Pafchek, R.

Paniccia, M.

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[CrossRef]

Passaro, V. M. N.

V. M. N. Passaro and F. Dell’Olio, “Scaling and optimization of MOS optical modulators in nanometer SOI waveguides,” IEEE Trans. NanoTechnol. 7(4), 401–408 (2008).
[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]

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]

Poon, A. W.

Poon, J. K. S.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

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]

Rooks, M. J.

Rubin, D.

Sacher, W. D.

Sadagopan, T.

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

Samara-Rubio, D.

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[CrossRef]

Sanchis, P.

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Sekaric, L.

Soltani, M.

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a silicon-on- insulator platform,” Opt. Express 17(4), 2247–2254 (2009).
[CrossRef] [PubMed]

Song, M.

Soref, R.

Su, Y.

Sun, G.

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]

Tummidi, R.

Vivien, L.

Vlasov, Y. A.

Webster, M. A.

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]

Willner, A. E.

Xinran, C.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Yan, C.

Yang, J.-Y.

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[CrossRef]

Ye, T.

Yegnanarayanan, S.

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a silicon-on- insulator platform,” Opt. Express 17(4), 2247–2254 (2009).
[CrossRef] [PubMed]

Zhang, B.

Zhang, L.

Zhou, L.

Zhou, Y.

Ziebell, M.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear Distortion in a Silicon Microring-Based Electro-Optic Modulator for Analog Optical Links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[CrossRef]

L. Ansheng, D. Samara-Rubio, L. Liao, and M. Paniccia, “Scaling the modulation bandwidth and phase efficiency of a silicon optical modulator,” IEEE J. Sel. Top. Quantum Electron. 11(2), 367–372 (2005).
[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]

IEEE Photon. Technol. Lett. (2)

T. Sadagopan, S. J. Choi, K. Djordjev, P. D. Dapkus, and S. J. Choi, “Carrier-induced refractive index changes in InP-based circular micro resonators for low-voltage high-speed modulation,” IEEE Photon. Technol. Lett. 17(2), 414–416 (2005).
[CrossRef]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[CrossRef]

IEEE Trans. NanoTechnol. (1)

V. M. N. Passaro and F. Dell’Olio, “Scaling and optimization of MOS optical modulators in nanometer SOI waveguides,” IEEE Trans. NanoTechnol. 7(4), 401–408 (2008).
[CrossRef]

J. Lightwave Technol. (4)

Nature (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Opt. Express (7)

C. Li, L. Zhou, and A. W. Poon, “Silicon microring carrier-injection-based modulators/switches with tunable extinction ratios and OR-logic switching by using waveguide cross-coupling,” Opt. Express 15(8), 5069–5076 (2007).
[CrossRef] [PubMed]

R. Soref, J. Guo, and G. Sun, “Low-energy MOS depletion modulators in silicon-on-insulator micro-donut resonators coupled to bus waveguides,” Opt. Express 19(19), 18122–18134 (2011).
[CrossRef] [PubMed]

Y. Li, L. Zhang, M. Song, B. Zhang, J.-Y. Yang, R. G. Beausoleil, A. E. Willner, and P. D. Dapkus, “Coupled-ring-resonator-based silicon modulator for enhanced performance,” Opt. Express 16(17), 13342–13348 (2008).
[CrossRef] [PubMed]

W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Optical modulation using anti-crossing between paired amplitude and phase resonators,” Opt. Express 15(25), 17264–17272 (2007).
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L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
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L. Zhang, J.-Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner, “Microring-based modulation and demodulation of DPSK signal,” Opt. Express 15(18), 11564–11569 (2007).
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Opt. Lett. (1)

Proc. IEEE (1)

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Other (5)

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “1-Vpp 10-Gb/s operation of slow-light silicon Mach-Zehnder modulator in wavelength range of 1 nm,” in IEEE Conference on Group IV Photonics 2010, pp. 45–47 (2010)

W. D. Sacher, W. M. Green, S. Assefa, T. Barwicz, S. M. Shank, Y. A. Vlasov, and J. Poon, “Controlled coupling in silicon microrings for high-speed, high extinction ratio, and low-chirp modulation,” in 2011 CLEO: Laser Applications to Photonic Applications, (CLEO, Baltimore, 2011), paper PDPA8.

M. A. Popović, “Resonant optical modulators beyond conventional energy efficiency and modulation frequency limitations,” in Conference on Integrated Photonics Research, Silicon and Nanophotonics (IPRSN) Monterey, CA (2010), paper IMC2.

J. Fujikata, J. Ushida, and M.-B. Yu, Z. ShiYang, D. Liang, P. L. Guo-Qiang, D.-L. Kwong, and T. Nakamura, “25 GHz operation of silicon optical modulator with projection MOS structure,” 2010 OFC: Collocated National Fiber Optic Engineers Conference, (OFC/NFOEC, San Diego 2010) paper OMI3.

L. S. Stewart and P. D. Dapkus, “In-plane thermally tuned silicon-on-insulator wavelength selective reflector,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IME2.

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Figures (6)

Fig. 1
Fig. 1

(a) notch design relies on ultra long photon lifetime to maintain constant energy amplitude while the intracavity energy may deplete as the coupling is zero during a long ‘1’ signal pattern; (b) the light drop design maintains the energy amplitude in the large ring resonator in a very small range by coupling light continuously from the lower waveguide into the large ring and modulating the upper waveguide to large ring coupling in a small range.

Fig. 2
Fig. 2

schematic diagram of the composite interferometer

Fig. 3
Fig. 3

(a) and (b) show the absolute coupling coefficient, intra-cavity energy amplitude and output signal power of the notch design and the proposed design respectively, which are obtained under the same time scale and the same received power; (c) and (d) show the ratio of max/min intracavity energy amplitude and the extinction ratio over the passive large ring propagation loss of notch design and the proprosed design.

Fig. 4
Fig. 4

(a) the proposed modulator’s bandwidth and the bandwidth of the modulator in [11] over the RC cutoff frequency; (b) the 3dB bandwidths over ring instrinsic loss of this design and [11], which shows that the tolearance to intrinsic loss is improved by the proposed design.

Fig. 5
Fig. 5

(a) BER curve of 40 Gb/s NRZ signals: the proposed modulator’s performance is comparable to the MZM, with a 2 dB power penalty. Its drive voltage is only 1/25 of the notch design. (b) The power penalty of the notch design and the modulator proposed by this paper over bit rate with RC constant equal to 5.68 ps. Modulation speed as 4 times as the main cavity linewidth can be achieved by the proposed modulator with power penalty no more than 2 dB. (c) The power penalty of the notch design and the modulator proposed by this paper over bit rate as the RC = 1 ps. Modulation speed more than 16 times as the main cavity linewidth can be achieved by the proposed modulator with power penalty less than 3 dB when the low Q ring phase shifter is biased 80 GHz off the laser frequency .

Fig. 6
Fig. 6

Signal pulses of 40 Gb/s RZ signals obtained using the time dependent model and the dynamic equations model agree with each other very well.

Equations (16)

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[ a 4 b 4 ] = [ t 2 κ 2 κ 2 * t 2 * ] [ γ e i ( θ + π ) 2 0 0 γ e i ( θ + π ) 2 ] [ t 1 κ 1 κ 1 * t 1 * ] [ a 1 b 1 ] = γ [ t κ κ * t * ] [ a 1 b 1 ]
t = i cos ( θ 2 ) , κ = i sin ( θ 2 )
d d t a ( t ) = [ j ω r ( 1 τ e 1 + 1 τ p ) 1 τ l ] a ( t ) + j μ 1 γ E i n
E o u t = E i n γ + j μ 1 γ a ( t )
a ( t ) = A ( t ) e j ω t
d d t A ( t ) = [ ( 1 τ e 1 + 1 τ p ) 1 τ l ] A ( t ) + j μ 1 γ E i n 0
E o u t 0 = E i n 0 γ + j μ 1 γ A ( t )
d d t A ( t ) = [ 1 τ p 1 τ l ] A ( t )
d d t A ( t ) = [ ( 1 τ e 1 + 1 τ p ) 1 τ l 1 τ e 2 ] A ( t ) + j μ 2 E i n 0
E o u t 0 = j μ 1 γ A ( t )
d A ( t ) d t = [ ( 1 τ e 1 + 1 τ p ) 1 τ l 1 τ e 2 ] A ( t ) + j μ 2 E i n 0
A ( t ) = j μ 2 E i n 0 [ ( 1 τ e 1 + 1 τ p ) + 1 τ l + 1 τ e 2 ]
d d t A ( t ) = [ 1 τ p 1 τ l 1 τ e 2 ] A ( t ) + j μ 2 E i n 0
A ( t ) = j μ 2 E i n 0 [ 1 τ p + 1 τ l + 1 τ e 2 ]
A min A max = 1 τ p + 1 τ l + 1 τ e 2 ( 1 τ e 1 + 1 τ p ) + 1 τ l + 1 τ e 2 = ( 1 τ p + 1 τ l + 1 τ e 2 ) 1 τ e 1 + ( 1 τ p + 1 τ l + 1 τ e 2 )
P = 3 4 C ( V p p ) 2 B R

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