Abstract

We investigated the linearity of graphene-based silicon waveguide modulators used in microwave photonics links. A theoretical model was developed to systematically analyze the linearity performance for the second-order harmonic distortions (SHD2) and the third-order intermodulation distortions (IMD3). For the graphene-based silicon waveguide electro-absorption (EA) modulator, the distortions were suppressed through bias optimization. As a result, the maximal spurious free dynamic range (SFDR) obtained for SHD2 and IMD3 were 105.9 dB ·Hz1/2 and 117.8 dB·Hz2/3, respectively. For the graphene-based silicon waveguide electro-refraction (ER) phase modulator, SHD2 was fully eliminated through the push-pull modulation and quadrature biasing, while the remaining IMD3 term was linearized by the proper adjustment of the bias voltage and phase shifter length to obtain an ultrahigh SFDR of 130 dB ·Hz2/3. Moreover, the graphene-based silicon waveguide ER modulator is more compact and tolerant to bias errors than a pure silicon modulator. These results reveal that the graphene-based silicon waveguide EA and ER modulators can be potentially utilized in integrated microwave photonics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (6)

Y. Yin, J. Li, Y. Xu, H. K. Tsang, and D. Dai, “Silicon-graphene photonic devices,” J. Semicond. 39, 061009 (2018).
[Crossref]

H. Shu, Y. Tao, M. Jin, X. Wang, and Z. Zhou, “A real-time tunable arbitrary power ratios graphene based power divider,” Sci. China Inf. Sci. 61, 080408 (2018).
[Crossref]

H. Shu, Z. Su, L. Huang, Z. Wu, X. Wang, Z. Zhang, and Z. Zhou, “Significantly high modulation efficiency of compact graphene modulator based on silicon waveguide,” Sci. Rep. 8, 991 (2018).

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
[Crossref]

Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
[Crossref]

M. Li, L. Wang, X. Li, X. Xiao, and S. Yu, “Silicon intensity mach–zehnder modulator for single lane 100 gb/s applications,” Photonics Res. 6, 109–116 (2018).
[Crossref]

2017 (2)

X. Yi, S. Chew, S. Song, L. Nguyen, and R. Minasian, “Integrated microwave photonics for wideband signal processing,” Photonics 4, 46 (2017).
[Crossref]

S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
[Crossref] [PubMed]

2016 (5)

A. Hosseinzadeh and C. T. Middlebrook, “Highly linear dual ring resonator modulator for wide bandwidth microwave photonic links,” Opt. Express 24, 27268–27279 (2016).
[Crossref] [PubMed]

A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High-performance and linear thin-film lithium niobate mach–zehnder modulators on silicon up to 50 ghz,” Opt. Lett. 41, 5700–5703 (2016).
[Crossref]

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Highly linear heterogeneous-integrated mach-zehnder interferometer modulators on si,” Opt. express 24, 19040–19047 (2016).
[Crossref] [PubMed]

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Ultralinear heterogeneously integrated ring-assisted mach–zehnder interferometer modulator on silicon,” Optica 3, 1483–1488 (2016).
[Crossref]

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

2015 (3)

C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 ghz bandwidth,” Nat. Photonics 9, 511 (2015).
[Crossref]

D. Conteduca, F. Dellolio, C. Ciminelli, and M. Armenise, “Resonant graphene-based tunable optical delay line,” IEEE Photonics J. 7, 1–9 (2015).
[Crossref]

R. A. Cohen, O. Amrani, and S. Ruschin, “Linearized electro-optic racetrack modulator based on double injection method in silicon,” Opt. Express 23, 2252–2261 (2015).
[Crossref] [PubMed]

2014 (2)

T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
[Crossref] [PubMed]

J. B. Khurgin and P. A. Morton, “Linearized bragg grating assisted electro-optic modulator,” Opt. Lett. 39, 6946–6949 (2014).
[Crossref]

2013 (5)

J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
[Crossref] [PubMed]

M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
[Crossref] [PubMed]

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

X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
[Crossref]

A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
[Crossref]

2012 (1)

L. Ming, Y. Xiaobo, and Z. Xiang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

2011 (3)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
[Crossref] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

A. Khilo, C. M. Sorace, and F. X. Kärtner, “Broadband linearized silicon modulator,” Opt. Express 19, 4485–4500 (2011).
[Crossref] [PubMed]

2010 (2)

S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

2009 (1)

J. Yao, “Microwave photonics,” J. Light. Technol. 27, 314–335 (2009).
[Crossref]

2008 (2)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
[Crossref] [PubMed]

V. M. Passaro and F. Dell Olio, “Scaling and optimization of mos optical modulators in nanometer soi waveguides,” IEEE Trans. Nanotechnol. 7, 401–408 (2008).
[Crossref]

2007 (2)

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

A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photonics Technol. Lett. 19, 312–314 (2007).
[Crossref]

2003 (1)

B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
[Crossref]

1995 (1)

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microwave Theory Tech. 43, 2184–2197 (1995).
[Crossref]

1987 (1)

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

Aamer, M.

A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
[Crossref]

Absil, P.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

Amrani, O.

R. A. Cohen, O. Amrani, and S. Ruschin, “Linearized electro-optic racetrack modulator based on double injection method in silicon,” Opt. Express 23, 2252–2261 (2015).
[Crossref] [PubMed]

Armenise, M.

D. Conteduca, F. Dellolio, C. Ciminelli, and M. Armenise, “Resonant graphene-based tunable optical delay line,” IEEE Photonics J. 7, 1–9 (2015).
[Crossref]

Assefa, S.

X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
[Crossref]

Asselberghs, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
[Crossref]

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

Ayazi, A.

M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
[Crossref] [PubMed]

Baehr-Jones, T.

M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
[Crossref] [PubMed]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

Basko, D. M.

S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
[Crossref]

Bennett, B.

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

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Bowers, J. E.

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Highly linear heterogeneous-integrated mach-zehnder interferometer modulators on si,” Opt. express 24, 19040–19047 (2016).
[Crossref] [PubMed]

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Ultralinear heterogeneously integrated ring-assisted mach–zehnder interferometer modulator on silicon,” Optica 3, 1483–1488 (2016).
[Crossref]

B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
[Crossref]

Brems, S.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

Bridges, W. B.

W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,” IEEE Trans. Microwave Theory Tech. 43, 2184–2197 (1995).
[Crossref]

Brimont, A.

A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
[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 (2007).
[Crossref]

Cardenas, J.

C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 ghz bandwidth,” Nat. Photonics 9, 511 (2015).
[Crossref]

J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
[Crossref] [PubMed]

C. T. Phare, J. Cardenas, Y. H. D. Lee, and M. Lipson, “Linear graphene on silicon nitride electroabsorption modulators for rf-over-fiber links,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. SF2G–2.
[Crossref]

Chang, W. S.

W. S. Chang, RF photonic technology in optical fiber links (Cambridge University, 2007).

Chen, J.

Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
[Crossref]

Chew, S.

X. Yi, S. Chew, S. Song, L. Nguyen, and R. Minasian, “Integrated microwave photonics for wideband signal processing,” Photonics 4, 46 (2017).
[Crossref]

Chiu, Y.-J.

B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
[Crossref]

Ciminelli, C.

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S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
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J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
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A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
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D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
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X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
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M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
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A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High-performance and linear thin-film lithium niobate mach–zehnder modulators on silicon up to 50 ghz,” Opt. Lett. 41, 5700–5703 (2016).
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X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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A. Hosseinzadeh and C. T. Middlebrook, “Highly linear dual ring resonator modulator for wide bandwidth microwave photonic links,” Opt. Express 24, 27268–27279 (2016).
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Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
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V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
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Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
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A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photonics Technol. Lett. 19, 312–314 (2007).
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C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Ultralinear heterogeneously integrated ring-assisted mach–zehnder interferometer modulator on silicon,” Optica 3, 1483–1488 (2016).
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C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Highly linear heterogeneous-integrated mach-zehnder interferometer modulators on si,” Opt. express 24, 19040–19047 (2016).
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J. B. Khurgin and P. A. Morton, “Linearized bragg grating assisted electro-optic modulator,” Opt. Lett. 39, 6946–6949 (2014).
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J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
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C. T. Phare, J. Cardenas, Y. H. D. Lee, and M. Lipson, “Linear graphene on silicon nitride electroabsorption modulators for rf-over-fiber links,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. SF2G–2.
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C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 ghz bandwidth,” Nat. Photonics 9, 511 (2015).
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D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
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Y. Yin, J. Li, Y. Xu, H. K. Tsang, and D. Dai, “Silicon-graphene photonic devices,” J. Semicond. 39, 061009 (2018).
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Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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Lipson, M.

C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 ghz bandwidth,” Nat. Photonics 9, 511 (2015).
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J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
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C. T. Phare, J. Cardenas, Y. H. D. Lee, and M. Lipson, “Linear graphene on silicon nitride electroabsorption modulators for rf-over-fiber links,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. SF2G–2.
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B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
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Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
[Crossref] [PubMed]

Liu, S.

Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
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Lo, G.-Q.

M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave mach-zehnder carrier depletion modulator based on differential drive,” Opt. Express 21, 3818–3825 (2013).
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Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
[Crossref]

Meric, I.

X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
[Crossref]

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A. Hosseinzadeh and C. T. Middlebrook, “Highly linear dual ring resonator modulator for wide bandwidth microwave photonic links,” Opt. Express 24, 27268–27279 (2016).
[Crossref] [PubMed]

Midrio, M.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
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X. Yi, S. Chew, S. Song, L. Nguyen, and R. Minasian, “Integrated microwave photonics for wideband signal processing,” Photonics 4, 46 (2017).
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C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Ultralinear heterogeneously integrated ring-assisted mach–zehnder interferometer modulator on silicon,” Optica 3, 1483–1488 (2016).
[Crossref]

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Highly linear heterogeneous-integrated mach-zehnder interferometer modulators on si,” Opt. express 24, 19040–19047 (2016).
[Crossref] [PubMed]

J. B. Khurgin and P. A. Morton, “Linearized bragg grating assisted electro-optic modulator,” Opt. Lett. 39, 6946–6949 (2014).
[Crossref]

J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
[Crossref] [PubMed]

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X. Yi, S. Chew, S. Song, L. Nguyen, and R. Minasian, “Integrated microwave photonics for wideband signal processing,” Photonics 4, 46 (2017).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319 (2007).
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V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
[Crossref]

Pantouvaki, M.

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

Paolella, A.

A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High-performance and linear thin-film lithium niobate mach–zehnder modulators on silicon up to 50 ghz,” Opt. Lett. 41, 5700–5703 (2016).
[Crossref]

Passaro, V. M.

V. M. Passaro and F. Dell Olio, “Scaling and optimization of mos optical modulators in nanometer soi waveguides,” IEEE Trans. Nanotechnol. 7, 401–408 (2008).
[Crossref]

Patil, A.

A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High-performance and linear thin-film lithium niobate mach–zehnder modulators on silicon up to 50 ghz,” Opt. Lett. 41, 5700–5703 (2016).
[Crossref]

Peters, J. D.

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Ultralinear heterogeneously integrated ring-assisted mach–zehnder interferometer modulator on silicon,” Optica 3, 1483–1488 (2016).
[Crossref]

C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, “Highly linear heterogeneous-integrated mach-zehnder interferometer modulators on si,” Opt. express 24, 19040–19047 (2016).
[Crossref] [PubMed]

Phare, C. T.

C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 ghz bandwidth,” Nat. Photonics 9, 511 (2015).
[Crossref]

C. T. Phare, J. Cardenas, Y. H. D. Lee, and M. Lipson, “Linear graphene on silicon nitride electroabsorption modulators for rf-over-fiber links,” in CLEO: Science and Innovations, (Optical Society of America, 2016), pp. SF2G–2.
[Crossref]

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B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
[Crossref]

Poitras, C. B.

J. Cardenas, P. A. Morton, J. B. Khurgin, A. Griffith, C. B. Poitras, K. Preston, and M. Lipson, “Linearized silicon modulator based on a ring assisted mach zehnder inteferometer,” Opt. Express 21, 22549–22557 (2013).
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Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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H. Shu, Y. Tao, M. Jin, X. Wang, and Z. Zhou, “A real-time tunable arbitrary power ratios graphene based power divider,” Sci. China Inf. Sci. 61, 080408 (2018).
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H. Shu, Z. Su, L. Huang, Z. Wu, X. Wang, Z. Zhang, and Z. Zhou, “Significantly high modulation efficiency of compact graphene modulator based on silicon waveguide,” Sci. Rep. 8, 991 (2018).

T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
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H. Shu, Z. Su, L. Huang, Z. Wu, X. Wang, Z. Zhang, and Z. Zhou, “Significantly high modulation efficiency of compact graphene modulator based on silicon waveguide,” Sci. Rep. 8, 991 (2018).

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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
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X. Yi, S. Chew, S. Song, L. Nguyen, and R. Minasian, “Integrated microwave photonics for wideband signal processing,” Photonics 4, 46 (2017).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
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Y. Yin, J. Li, Y. Xu, H. K. Tsang, and D. Dai, “Silicon-graphene photonic devices,” J. Semicond. 39, 061009 (2018).
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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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M. Li, L. Wang, X. Li, X. Xiao, and S. Yu, “Silicon intensity mach–zehnder modulator for single lane 100 gb/s applications,” Photonics Res. 6, 109–116 (2018).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
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S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
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T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
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Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
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Zhang, L.

S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
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Zhang, Q.

Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
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Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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Zhang, Z.

H. Shu, Z. Su, L. Huang, Z. Wu, X. Wang, Z. Zhang, and Z. Zhou, “Significantly high modulation efficiency of compact graphene modulator based on silicon waveguide,” Sci. Rep. 8, 991 (2018).

Zheng, L.

S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
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S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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Zhou, L.

Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
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Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
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Zhou, Z.

H. Shu, Y. Tao, M. Jin, X. Wang, and Z. Zhou, “A real-time tunable arbitrary power ratios graphene based power divider,” Sci. China Inf. Sci. 61, 080408 (2018).
[Crossref]

H. Shu, Z. Su, L. Huang, Z. Wu, X. Wang, Z. Zhang, and Z. Zhou, “Significantly high modulation efficiency of compact graphene modulator based on silicon waveguide,” Sci. Rep. 8, 991 (2018).

T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, “Demonstration of 6.25 gbaud advanced modulation formats with subcarrier multiplexed technique on silicon mach-zehnder modulator,” Opt. Express 22, 19818–19823 (2014).
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Zhu, H.

Y. Zhou, L. Zhou, S. Liu, H. Zhu, M. Wang, X. Li, and J. Chen, “Linearity characterization of a dual-parallel mach-zehnder modulator,” in Optical Fiber Communication Conference, (Optical Society of America, 2016), pp. W2A–28.
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S. Shao, J. Ding, L. Zheng, K. Zou, L. Zhang, F. Zhang, and L. Yang, “Optical pam-4 signal generation using a silicon mach-zehnder optical modulator,” Opt. Express 25, 23003–23013 (2017).
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ACS Nano (1)

S. Zhipei, H. Tawfique, T. Felice, P. Daniel, P. Giulia, W. Fengqiu, B. Francesco, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4, 803–810 (2010).
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IEEE J. Quantum Electron. (1)

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

D. Conteduca, F. Dellolio, C. Ciminelli, and M. Armenise, “Resonant graphene-based tunable optical delay line,” IEEE Photonics J. 7, 1–9 (2015).
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Q. Zhang, H. Yu, H. Jin, T. Qi, Y. Li, J. Yang, and X. Jiang, “Linearity comparison of silicon carrier-depletion-based single, dual-parallel, and dual-series mach–zehnder modulators,” J. Light. Technol. 36, 3318–3331 (2018).
[Crossref]

A. M. Gutierrez, A. Brimont, J. Herrera, M. Aamer, D. J. Thomson, F. Y. Gardes, G. T. Reed, J.-M. Fedeli, and P. Sanchis, “Analytical model for calculating the nonlinear distortion in silicon-based electro-optic mach–zehnder modulators,” J. Light. Technol. 31, 3603–3613 (2013).
[Crossref]

B. Liu, J. Shim, Y.-J. Chiu, A. Keating, J. Piprek, and J. E. Bowers, “Analog characterization of low-voltage mqw traveling-wave electroabsorption modulators,” J. Light. Technol. 21, 3011 (2003).
[Crossref]

J. Yao, “Microwave photonics,” J. Light. Technol. 27, 314–335 (2009).
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J. Semicond. (1)

Y. Yin, J. Li, Y. Xu, H. K. Tsang, and D. Dai, “Silicon-graphene photonic devices,” J. Semicond. 39, 061009 (2018).
[Crossref]

Laser Photonics Rev. (2)

Y. Hu, M. Pantouvaki, J. Van Campenhout, S. Brems, I. Asselberghs, C. Huyghebaert, P. Absil, and D. Van Thourhout, “Broadband 10 gb/s operation of graphene electro-absorption modulator on silicon,” Laser Photonics Rev. 10, 307–316 (2016).
[Crossref]

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
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Nano Lett. (1)

L. Ming, Y. Xiaobo, and Z. Xiang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
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Nat. Photonics (6)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
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V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. Van Campenhout, C. Huyghebaert, I. Goykhman, A. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12, 40 (2018).
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X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
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Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64 (2011).
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Opt. Express (7)

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Figures (13)

Fig. 1
Fig. 1 (a) Schematic cross-sections of the graphene-based silicon waveguide modulators containing single (a) and double (b) graphene layers.
Fig. 2
Fig. 2 Simulated attenuation coefficient α and variation of the real effective index Δneff plotted as functions of the driving voltage for the single-layer graphene modulator. The thickness of the Al2O3 insulation layer is set to 10 nm (n=1.732,ε = 9).
Fig. 3
Fig. 3 Schematic of the microwave photonic link using graphene-based silicon waveguide modulator. The red and blue line are optical connect and electrical RF connect, respectively.
Fig. 4
Fig. 4 (a) Schematic of the graphene EA modulator. (b) Steady-state normalized transmission as a function of the driving voltage.
Fig. 5
Fig. 5 Linearity features of the graphene EA modulator. (a) FUND, SHD2 and IMD3 powers plotted as functions of the DC voltage at an input power of 0 dBm (v0 = 0.316 V). (b) CDR2 and CDR3 values as functions of DC voltage at an input power of 0 dBm. (c) SFDR values for SHD2 and IMD3 plotted at different DC voltages.
Fig. 6
Fig. 6 (a) SFDR for IMD3 plotted as functions of DC voltage for the Si-SLG, Si-DLG, and Si3N4-DLG modulators. The thickness of the insulation layer and active length are set to 10 nm and 100 μm, respectively. (b) Optimized SFDR values for IMD3 and SHD2 plotted as functions of the thickness of the insulation layer in the Si-SLG structure. The material parameters of HfO2 used in the simulation are n = 2.07, ε = 18.
Fig. 7
Fig. 7 (a) Maximal SFDR for IMD3 obtained for the Si-SLG modulator with a 14-nm Al2O3 insulation layer. (b) Maximal SFDR for SHD2 obtained for the Si-SLG modulator with a 16-nm HfO2 insulation layer. The intercept points are also displayed in the figures.
Fig. 8
Fig. 8 (a) Schematic of the graphene ER modulator based on the unbalanced MZI. (b) Steady-state normalized transmission as a function of the DC voltage.
Fig. 9
Fig. 9 (a) SHD2 distortion power plotted as a function of the phase shifter length at a DC bias voltage of 7 V and input power of 0 dBm (v0 = 0.316 V). (b) Power contours of the FUND and IMD3 components obtained as functions of the bias voltage VDC and phase shifter length L at an input power of 0 dBm.
Fig. 10
Fig. 10 Contour maps of the SFDR for the IMD3 distortion obtained at different DC voltages and phase shifter lengths under the bias condition Φbias = π/2. From the left to the right: (a) Si-SLG, (b) Si-DLG, and (c) Si3N4-DLG. The marked points denote the maximum SFDR values.
Fig. 11
Fig. 11 SFDR for IMD3 plotted as a function of the phase shifter length under the corresponding optimum DC voltage and Φbias = π/2.
Fig. 12
Fig. 12 Maximal SFDR for IMD3 of the graphene ER modulator. The intercept points are also displayed in the figure.
Fig. 13
Fig. 13 (a) Variations of the effective index Δneff plotted at different voltages for the graphene-based modulator and pure silicon modulators. (b) Linearity degradations of the graphene modulators and five typical silicon modulators observed when the DC voltage deviates from the optimum bias voltage. The device length for each modulator is set to the optimal value.

Tables (3)

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Table 1 Parameters of the microwave photonic link used in the calculations.

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Table 2 Four typical design schemes of the carrier-depletion silicon modulator

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Table 3 Linearity comparison of the graphene EA, graphene ER, and silicon FCD modulators

Equations (23)

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σ ( ω , μ c , τ , T ) = j e 2 ( ω j τ 1 ) π 2 [ 1 ( ω j τ 1 ) 2 0 + ξ ( f d ( ξ ) ξ f d ( ξ ) ξ ) d ξ 0 + f d ( ξ ) f d ( ξ ) ( ω j τ 1 ) 2 4 ( ξ / ) 2 d ξ ]
μ c = v F η π | V g V dirac |
α ( V ) = a 0 + a 1 V + a 2 V 2 + a 3 V 3 + a 4 V 4 + O ( V 4 )
Δ n eff ( V ) = b 1 V + b 2 V 2 + b 3 V 3 + b 4 V 4 + O ( V 4 )
V = V DC + v rf = V DC + v 0 ( cos 2 π f 1 t + cos 2 π f 2 t )
Y EA ( V ) = exp ( 2 α L ) = exp [ 2 L ( a 0 + a 1 V + a 2 V 2 + a 3 V 3 + a 4 V 4 ) ]
Δ Φ = Δ Φ bias + Δ Φ graphene = Δ Φ bias + 2 π λ L Δ n eff
Y ER ( V ) = 1 2 { 1 + cos [ Δ Φ bias + 2 π λ L ( b 1 V + b 2 V 2 + b 3 V 3 + b 4 V 4 ) ] }
T FUND = v 0 d Y d V | V = V DC + 3 8 v 0 3 d 3 Y d V 3 | V = V DC + 5 96 v 0 5 d 5 Y d V 5 | V = V DC + O ( v 0 5 )
T SHD 2 = 1 4 v 0 2 d 2 Y d V 2 | V = V DC + 5 96 v 0 4 d 4 Y d V 4 | V = V DC + O ( v 0 4 )
T IMD 3 = 1 8 v 0 3 d 3 Y d V 3 | V = V DC + 5 192 v 0 5 d 5 Y d V 5 | V = V DC + O ( v 0 5 )
CDR 2 = P FUND P SHD 2 , CDR 3 = P FUND P IMD 3
SFDR 2 = P FUND | P SHD 2 = NF NF , SFDR 3 = P FUND | P IMD 3 = NF NF
Y ( V ) = Y ( V DC ) exp [ 2 L Δ α ( v rf ) ]
Δ α ( v rf ) = k 1 v rf + k 2 v rf 3 + k 3 v rf 3 + k 4 v rf 4
k 1 = 4 a 4 V DC 3 + 3 a 3 V DC 2 + 2 a 2 V DC + a 1 k 2 = 6 a 4 V DC 2 + 3 a 3 V DC + a 2 k 3 = 4 a 4 V DC + a 3 k 4 = a 4
P SHD 2 R D 2 [ P L L 0 r D k 2 v 0 2 ] 2
P IMD 3 R D 2 [ P L L 0 r D 3 4 k 3 v 0 3 ] 2
Δ Φ = Δ Φ bias + 2 π λ L [ Δ n eff ( V DC + v rf ) Δ n eff ( V DC + v rf ) ]
Δ Φ ( v rf ) = k 1 v rf + k 3 v rf 3
k 1 = 2 π λ L ( 8 b 4 V DC 3 + 6 b 3 V DC 3 + 4 b 2 V DC + 2 b 1 ) k 3 = 2 π λ L ( 8 b 4 V DC + 2 b 3 )
Y ( V ) = 1 2 { 1 Δ Φ ( v rf ) + 1 3 ! Δ Φ ( v rf ) 3 + O [ Δ Φ ( v rf ) 3 ] } = 1 2 [ 1 k 1 v rf + ( 1 6 k 1 3 k 3 ) v rf 3 + 1 2 k 1 2 k 3 v rf 5 + 1 2 k 1 k 3 2 v rf 7 + 1 6 k 3 3 v rf 9 + O ( v rf 9 ) ]
P IMD 3 R D 2 [ P L L 0 r D 3 8 v 0 3 ( 1 6 k 1 3 k 3 ) ] 2

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