Abstract

The efficiency of optical sideband generation with a microring resonator modulator as a function of modulator parameters is studied taking into account the photon dynamics inside the resonator. The best achievable modulation efficiency is determined for any choice of the resonator intrinsic quality factor, and analytic solutions for the optimum modulator parameters, namely the coupling coefficient and the detuning between the frequencies of the input laser light and the microring resonance, are provided. This analysis is carried out both for a narrowband RF signal, in which case the modulator is optimized for the center frequency of this signal, and for wideband signals, when high conversion efficiency over a wide range of RF frequencies is desired. The obtained results are expected to be useful coherent optical links, direct detection RF receivers, and optical wavelength converters

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
    [Crossref]
  2. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
    [Crossref]
  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, 185–191 (2010).
    [Crossref]
  4. A. Ayazi, T. Baehr-Jones, Y. Liu, A. Eu-Jin Lim, and M. Hochberg, “Linearity of silicon ring modulators for analog optical links,” Opt. Express 20, 13115–13122 (2012).
    [Crossref] [PubMed]
  5. W. D. Sacher and J. K. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16, 15741–15753 (2008).
    [Crossref] [PubMed]
  6. 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, 149–158 (2010).
    [Crossref]
  7. J. Müller, F. Merget, S Sharif Azadeh, J. Hauck, S Romero Garcia, B. Shen, and J. Witzens,“ Optical peaking enhancement in high-speed ring modulators,” Sci. Rep. 4, 6310 (2014).
    [Crossref] [PubMed]
  8. H. Yu, D. Ying, M. Pantouvaki, J. Van Campenhout, P. Absil, Y. Hao, J. Yang, and X. Jiang, “Trade-off between optical modulation amplitude and modulation bandwidth of silicon micro-ring modulators,” Opt. Express 22(12), 15178–15189 (2014).
    [Crossref] [PubMed]
  9. B. Pile and G. Taylor, “Small-signal analysis of microring resonator modulators,” Opt. Express 22(12), 14913–14928 (2014).
    [Crossref] [PubMed]
  10. 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 (IEEE, 2014), pp. 47–48.
  11. R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
    [Crossref]
  12. S. Karimelahi and A. Sheikholeslami, “Ring modulator small-signal response analysis based on pole-zero representation,” Opt. Express 24, 7585–7599 (2016).
    [Crossref] [PubMed]
  13. M. Hossein-Zadeh, “Photonic microwave receivers based on high-Q optical resonance,” in SPIE LASE (International Society for Optics and Photonics, 2012), paper 82360T.
  14. V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
    [Crossref]
  15. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
    [Crossref]
  16. E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
    [Crossref]
  17. M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
    [Crossref]
  18. M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
    [Crossref]
  19. R. Esman and K. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,” IEEE Photonics Technol. Lett. 7, 218–220 (1995).
    [Crossref]
  20. M. T. Wade, X. Zeng, and M. Popović, “Wavelength conversion in modulated coupled-resonator systems and their design via an equivalent linear filter representation,” Opt. Lett. 40(1), 107–110 (2015).
    [Crossref]
  21. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  22. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [Crossref]
  23. Y. Ehrlichman, N. Dostart, and M. A. Popović, “Dual-cavity resonant modulators for efficient narrowband RF/microwave photonics,” in 2016 IEEE International Topical Meeting on Microwave Photonics (MWP) (2016), pp. 165-168.
  24. C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
    [Crossref]

2016 (2)

S. Karimelahi and A. Sheikholeslami, “Ring modulator small-signal response analysis based on pole-zero representation,” Opt. Express 24, 7585–7599 (2016).
[Crossref] [PubMed]

C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
[Crossref]

2015 (2)

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

M. T. Wade, X. Zeng, and M. Popović, “Wavelength conversion in modulated coupled-resonator systems and their design via an equivalent linear filter representation,” Opt. Lett. 40(1), 107–110 (2015).
[Crossref]

2014 (3)

2013 (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

2012 (1)

2010 (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, 185–191 (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, 149–158 (2010).
[Crossref]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

2008 (2)

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

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

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[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, 998–1005 (1997).
[Crossref]

1995 (1)

R. Esman and K. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,” IEEE Photonics Technol. Lett. 7, 218–220 (1995).
[Crossref]

1994 (1)

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[Crossref]

1993 (2)

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
[Crossref]

Absil, P.

Ackerman, E.

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

Ayazi, A.

Baehr-Jones, T.

Ban, Y.

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 (IEEE, 2014), pp. 47–48.

Beausoleil, R. G.

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, 185–191 (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, 149–158 (2010).
[Crossref]

Bois, A.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Capmany, J.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Caverley, M.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Chang, W.

M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
[Crossref]

Charczenko, W.

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[Crossref]

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 (IEEE, 2014), pp. 47–48.

Choi, W.-Y.

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 (IEEE, 2014), pp. 47–48.

Chrostowski, L.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[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, 998–1005 (1997).
[Crossref]

Daryoush, A.

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

Dostart, N.

Y. Ehrlichman, N. Dostart, and M. A. Popović, “Dual-cavity resonant modulators for efficient narrowband RF/microwave photonics,” in 2016 IEEE International Topical Meeting on Microwave Photonics (MWP) (2016), pp. 165-168.

Dube-Demers, R.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Ehrlichman, Y.

Y. Ehrlichman, N. Dostart, and M. A. Popović, “Dual-cavity resonant modulators for efficient narrowband RF/microwave photonics,” in 2016 IEEE International Topical Meeting on Microwave Photonics (MWP) (2016), pp. 165-168.

Esman, R.

R. Esman and K. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,” IEEE Photonics Technol. Lett. 7, 218–220 (1995).
[Crossref]

Eu-Jin Lim, A.

Farwell, M.

M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
[Crossref]

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, 998–1005 (1997).
[Crossref]

Georgas, M.

C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
[Crossref]

Hamilton, M.

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[Crossref]

Hao, Y.

Hauck, J.

J. Müller, F. Merget, S Sharif Azadeh, J. Hauck, S Romero Garcia, 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, 998–1005 (1997).
[Crossref]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Heideman, R.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

Hochberg, M.

Hossein-Zadeh, M.

M. Hossein-Zadeh, “Photonic microwave receivers based on high-Q optical resonance,” in SPIE LASE (International Society for Optics and Photonics, 2012), paper 82360T.

Huber, D.

M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
[Crossref]

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Jiang, X.

Karimelahi, S.

Kasemset, D.

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

LaGasse, M.

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[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, 998–1005 (1997).
[Crossref]

LaRochelle, S.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

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 (IEEE, 2014), pp. 47–48.

Leinse, A.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

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, 149–158 (2010).
[Crossref]

Liang, W.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[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, 998–1005 (1997).
[Crossref]

Liu, Y.

Maleki, L.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Marpaung, D.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Merget, F.

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

Müller, J.

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

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

Pantouvaki, M.

Pile, B.

Plant, D.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Poon, J. K.

Popovic, M.

Popovic, M. A.

Y. Ehrlichman, N. Dostart, and M. A. Popović, “Dual-cavity resonant modulators for efficient narrowband RF/microwave photonics,” in 2016 IEEE International Topical Meeting on Microwave Photonics (MWP) (2016), pp. 165-168.

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

Romero Garcia, S

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

Sacher, W. D.

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

Samant, N.

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Seidel, D.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Sharif Azadeh, S

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

Sheikholeslami, A.

Shen, B.

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

Shi, W.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Solomatine, I.

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

Song, M.

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, 185–191 (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, 149–158 (2010).
[Crossref]

St-Yves, J.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Sun, C.

C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
[Crossref]

Taylor, G.

Thaniyavarn, S.

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[Crossref]

Van Campenhout, J.

Wade, M.

C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
[Crossref]

Wade, M. T.

Wang, Y.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Wanuga, S.

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

Williams, K.

R. Esman and K. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,” IEEE Photonics Technol. Lett. 7, 218–220 (1995).
[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, 149–158 (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, 185–191 (2010).
[Crossref]

Witzens, J.

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

Yang, J.

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, 149–158 (2010).
[Crossref]

Ying, D.

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 (IEEE, 2014), pp. 47–48.

Yu, H.

Zeng, X.

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, 149–158 (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, 185–191 (2010).
[Crossref]

Zhong, Q.

R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

Electron. Lett. (1)

M. LaGasse, W. Charczenko, M. Hamilton, and S. Thaniyavarn, “Optical carrier filtering for high dynamic range fibre optic links,” Electron. Lett. 30, 2157–2158 (1994).
[Crossref]

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

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, 185–191 (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, 149–158 (2010).
[Crossref]

IEEE J. Solid-State Circuits (1)

C. Sun, M. Wade, M. Georgas, and et al., “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51, 893-907 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (2)

R. Esman and K. Williams, “Wideband efficiency improvement of fiber optic systems by carrier subtraction,” IEEE Photonics Technol. Lett. 7, 218–220 (1995).
[Crossref]

M. Farwell, W. Chang, and D. Huber, “Increased linear dynamic range by low biasing the Mach-Zehnder modulator,” IEEE Photonics Technol. Lett. 5, 779–782 (1993).
[Crossref]

IEEE Photonics Technology Letters (1)

V. S. Ilchenko, A. B. Matsko, I. Solomatine, A. A. Savchenkov, D. Seidel, and L. Maleki, “Ka–Band All-Resonant Photonic Microwave Receiver,” IEEE Photonics Technology Letters 20, 1600-1612 (2008).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

E. Ackerman, S. Wanuga, D. Kasemset, A. Daryoush, and N. Samant, “Maximum dynamic range operation of a microwave external modulation fiberoptic link,” IEEE Trans. Microw. Theory Tech. 41, 1299–1306 (1993).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Single-Sideband Electro-Optical Modulator and Tunable Microwave Photonic Receiver,” IEEE Trans. Microw. Theory Techn. 58, 3167-3174 (2010).
[Crossref]

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R. Dube-Demers, J. St-Yves, A. Bois, Q. Zhong, M. Caverley, Y. Wang, L. Chrostowski, S. LaRochelle, D. Plant, and W. Shi, “Analytical modeling of silicon microring and microdisk modulators with electrical and optical dynamics,” J Lightwave Technol. 33, 4240–4252 (2015).
[Crossref]

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

Opt. Express (5)

Opt. Lett. (1)

Sci. Rep. (1)

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

Other (4)

M. Hossein-Zadeh, “Photonic microwave receivers based on high-Q optical resonance,” in SPIE LASE (International Society for Optics and Photonics, 2012), paper 82360T.

Y. Ehrlichman, N. Dostart, and M. A. Popović, “Dual-cavity resonant modulators for efficient narrowband RF/microwave photonics,” in 2016 IEEE International Topical Meeting on Microwave Photonics (MWP) (2016), pp. 165-168.

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 (IEEE, 2014), pp. 47–48.

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Figures (10)

Fig. 1
Fig. 1 (a) The microring resonator modulator studied in this work. (b) The spectra of the optical input sin, applied RF signal vRF, and the output optical signal sout with multiple sidebands generated by the modulator. The modulator is considered as a mixer which upconverts the input RF signal at frequency Ω into the optical signal ωl + Ω, which is the first sideband of the output signal sout.
Fig. 2
Fig. 2 (a) The Lorentzian profile Λ(ω) as defined by Eq. (9), describing resonant enhancement in the microring resonator; the red and the blue arrows indicate the input laser carrier at frequency ωl and the generated sideband at frequency ωl + Ω, respectively. In this example, laser detuning δω = ωlωo is assumed to be negative. (b) The conversion efficiency G as a function of applied RF frequency Ω.
Fig. 3
Fig. 3 (a) The optimum frequency detuning δω as given by Eqs. (10), (11) which maximizes the conversion efficiency at frequency Ωo shown along the x-axis. (b) Location of the laser frequency ωl and the sideband frequency ωl + Ωo relative to the Lorentzian resonance of the microring centered at ωo for several representative points from plot (a).
Fig. 4
Fig. 4 The conversion efficiency G as a function of coupling rate re (normalized by loss rate ro) and frequency detuning δω (normalized by RF frequency Ωo) as given by Eq. (6). Plot (a) represents the case when Ω o Δ ω 3 d B ( o ) (with this particular plot created for Ω o = Δ ω 3 d B ( o ) / 2 ), and (b) represents the case when Ω o > Δ ω 3 d B ( o ) (with this particular plot created for Ω o = 2 Δ ω 3 d B ( o ) ). Without loss of generality, δ ω m / Δ ω 3 d B ( o ) = 1 is assumed.
Fig. 5
Fig. 5 (a) Solid red curve: the maximum conversion efficiency Gmaxo) achievable in the modulator optimized for frequency Ωo, with Ω o / Δ ω 3 d B ( o ) plotted along the x-axis. Dashed curves: conversion efficiency profiles G(Ω) for modulators optimized for 3 different frequencies Ωo, with the respective values of Ωo indicated by circles and Ω / Δ ω 3 d B ( o ) plotted along the x-axis. The resonant frequency swing δωm equal to the intrinsic linewidth Δ ω 3 d B ( o ) is assumed. (b) The maximum conversion efficiency Gmax vs. non-normalized frequency Ωo for 4 values of Δ ω 3 d B ( o ), with modulation frequency swing δωm/2π = 1 GHz.
Fig. 6
Fig. 6 (a) An example of frequency response G(Ω) of the modulator optimized for maximum efficiency at Ωo. 3dB bandwidth BW is defined as the bandwidth around Ωo within which the response goes down by no more than 3dB with respect to the response at the center frequency Go). (b) The bandwidth BW normalized by center frequency Ωo in the modulator optimized for Ωo as a function of Ωo, as given by Eq. (15).
Fig. 7
Fig. 7 A representative frequency response G(Ω) of a resonant modulator, indicating the response metrics used in modulator design optimization for baseband RF signals. The x-axis is the frequency Ω in logarithmic scale. Plots of G(Ω) with x axis in linear scale can be found in Fig. 2(b) and Fig. 6(a).
Fig. 8
Fig. 8 Conversion efficiency GDC (in dB) as a function of the required minimum 3 dB bandwidth Ω 3 d B m i n and coupling rate re normalized by loss rate ro. The white lines are the contour lines of the obtained ripple values for the obtained ripple value α = 0, 1, 3, and 6 dB. Red circles indicate the designs with the best efficiency for several fixed values of Ω 3 d B m i n, assuming the ripple α is not constrained. The efficiencies are calculated for δ ω m / Δ ω 3 d B ( o ) = 1. The formulas used to create this plot can be found in the Appendix.
Fig. 9
Fig. 9 The conversion efficiency GDC (in dB) for modulators optimized to have the 3 dB bandwidth of at least the Ω 3 d B m i n value shown along the x axis, and the ripple of at most αmax shown along the y axis. Both detuning δω and coupling rate re are optimized at each point; the analytic solutions are given in the Appendix. The white line labeled the “optimum ripple” indicates the optimum ripple α which maximizes the efficiency for given Ω 3 d B / δ ω 3 d B ( o ). Without loss of generality δ ω m / δ ω 3 d B ( o ) = 1 is assumed.
Fig. 10
Fig. 10 The conversion efficiency GDC for modulators optimized for given minimum 3 dB bandwidth Ω 3 d B m i n for several values of the required maximum ripple αmax. Three sets of curves are for different loss rates ro. Modulation frequency swing δωm/2π = 1 GHz.

Equations (33)

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G = | S o u t ( ω l + Ω ) | 2 | S i n ( ω l ) | 2 ,
d a d t = ( j ω o + j δ ω m 2 cos ( Ω t ) r o r e ) a j 2 r e s i n ,
s o u t = s i n j 2 r e a .
s o u t s i n = 1 2 r e m = J m ( δ ω m 2 Ω ) e j m Ω t × n = ( 1 ) n J n ( δ ω m 2 Ω ) e j n Ω t j δ ω + r e + r o + j n Ω ,
δ ω = ω l ω o
S o u t ( ω l + Ω ) s i n ( ω l ) = 2 r e J 0 ( δ ω m 2 Ω ) J 1 ( δ ω m 2 Ω ) e j Ω t ( 1 j δ ω + r e + r o + j Ω 1 j δ ω + r e + r o ) δ ω m r e 2 Ω e j Ω t ( 1 j δ ω + r e + r o + j Ω 1 j δ ω + r e + r o ) ,
G = ( δ ω m r e / 2 ) 2 [ δ ω 2 + ( r e + r o ) 2 ] [ ( δ ω + Ω ) 2 + ( r e + r o ) 2 ] .
G = ( δ ω m r e / 2 ) 2 [ δ ω 2 + ( r e + 1 ) 2 ] [ ( δ ω + Ω ) 2 + ( r e + 1 ) 2 ] ,
G = [ δ ω m r e / 2 ( r e + r o ) 2 ] 2 Λ ( δ ω ) Λ ( δ ω + Ω ) ,
Λ ( δ ω ) ( r e + r o ) 2 δ ω 2 + ( r e + r o ) 2
δ ω = Ω o 2 , G = ( δ ω m r e / 2 ) 2 [ ( r e + r o ) 2 + ( Ω o 2 ) 2 ] 2 if Ω o Δ ω 3 d B ,
δ ω 1 , 2 = Ω o 2 ± ( Ω o 2 ) 2 ( r e + r o ) 2 , G = ( δ ω m r e / 2 ) 2 ( r e + r o ) 2 Ω o 2 if Ω o > Δ ω 3 d B ,
Δ ω 3 d B 2 ( r e + r o ) .
Δ ω 3 d B ( o ) 2 r o
r e o p t = r o 2 + ( Ω o / 2 ) 2 , δ ω = Ω o / 2 .
G m a x = [ δ ω m r e o p t / 2 ( r e o p t + r o ) 2 + ( Ω o / 2 ) 2 ] 2 = [ δ ω m r e o p t / 2 ( Δ ω 3 d B / 2 ) 2 + ( Ω o / 2 ) 2 ] 2 .
G m a x ( Ω o ) = ( δ ω m 2 Ω o ) 2 .
G m a x ( Ω o 0 ) = 1 16 ( δ ω m Δ ω 3 d B ( o ) ) 2 .
Ω 3 d B = δ ω + 2 δ ω 2 + ( r e + r o ) 2 .
Ω 3 d B = Ω o 2 + Ω o 2 + 2 ( r e + r o ) 2 2 .
B W = 2 ( Ω 3 d B Ω o ) = 2 Ω o 2 + 2 ( r e + r o ) 2 2 Ω o ,
B W ( Ω o ) = ( 3 1 ) Ω o 0.73 Ω o .
G D C = ( δ ω m r e / 2 ) 2 [ δ ω 2 + ( r e + r o ) 2 ] 2 ;
α = G m a x / G D C .
α = δ ω 2 + ( r e + r o ) 2 ( r e + r o ) 2 .
δ ω = ( r e + r o ) α 1 ,
x Ω 3 d B m i n Δ ω 3 d B / 2 = Ω 3 d B m i n ( r e + r o )
α = 1 , G D C = ( δ ω m r e / 2 ) 2 ( r e + r o ) 4 .
α = 3 x 2 2 x 2 x 2 1 , G D C = ( δ ω m r e / 2 ) 2 [ α ( r e + r o ) 2 ] 2 .
α = 1 , r e = r o , G D C = 1 16 ( δ ω m 2 r o ) 2 .
r e = 6 Ω 3 d B m i n 2 ( 3 r o 2 4 r o 2 + Ω 3 d B m i n 2 ) 16 r o Ω 3 d B m i n 2 + 8 r o 3 8 r o 2 + 18 Ω 3 d B m i n 2 ,
r e = Ω 3 d B m i n α m a x 1 + 2 α m a x 1 , α = α m a x .
G D C = ( δ ω m r e / 2 ) 2 [ α ( r e + r o ) 2 ] 2 .

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