Abstract

Silicon photonic wavelength division multiplexing (WDM) transceivers promise to achieve multi-Tbps data rates for next-generation short-reach optical interconnects. In these systems, microring resonators are important because of their low power consumption and small footprint, two critical factors for large-scale WDM systems. However, their resonant nature and silicon’s strong optical nonlinearity give rise to nonlinear effects that can deteriorate the system’s performance with optical powers on the order of milliwatts, which can be reached on the transmitter side where a laser is directly coupled into resonant modulators. Here, a theoretical time-domain nonlinear model for the dynamics of optical power in silicon resonant modulators is derived, accounting for two-photon absorption, free-carrier absorption and thermal and dispersion effects. This model is used to study the effects of high input optical powers over modulation quality, and experimental data in good agreement with the model is presented. Two major consequences are identified: the importance of a correct initialization of the resonance wavelength with respect to the laser due to the system’s bistability; and the existence of an optimal input optical power beyond which the modulation quality degrades.

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

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References

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2016 (2)

L. Alloatti, D. Cheian, and R. J. Ram, “High-speed modulator with interleaved junctions in zero-change CMOS photonics,” Appl. Phys. Lett. 108(13), 131101 (2016).
[Crossref]

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

2014 (1)

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014).
[Crossref]

2013 (1)

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

2012 (2)

2008 (1)

2007 (1)

2006 (2)

2005 (3)

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

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-raman lasers and micro-parametric oscillators,” Opt. Express 13(9), 3558–3566 (2005).
[Crossref]

2004 (1)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

2000 (1)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

1997 (1)

L. Shampine and M. Reichelt, “The MATLAB ODE suite,” SIAM J. Sci. Comput. 18(1), 1–22 (1997).
[Crossref]

1991 (1)

G. Treyz, “Silicon Mach-Zehnder waveguide interferometers operating at 1.3 $\mu$μm,” Electron. Lett. 27(2), 118–120 (1991).
[Crossref]

1990 (1)

C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. on Sel. Areas Commun. 8(6), 948–964 (1990).
[Crossref]

1987 (1)

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

Adibi, A.

M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 2011).

Alloatti, L.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

L. Alloatti, D. Cheian, and R. J. Ram, “High-speed modulator with interleaved junctions in zero-change CMOS photonics,” Appl. Phys. Lett. 108(13), 131101 (2016).
[Crossref]

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), pp. 1–3 (2017).

Almeida, V. R.

Asanovic, K.

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

Atabaki, A. H.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), pp. 1–3 (2017).

Batten, C.

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

Beamer, S.

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

Bennett, B.

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

Biberman, A.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014).
[Crossref]

Borselli, M.

Brackett, C. A.

C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. on Sel. Areas Commun. 8(6), 948–964 (1990).
[Crossref]

Carmon, T.

Cheian, D.

L. Alloatti, D. Cheian, and R. J. Ram, “High-speed modulator with interleaved junctions in zero-change CMOS photonics,” Appl. Phys. Lett. 108(13), 131101 (2016).
[Crossref]

Claps, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Cunningham, J. E.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

de Cea, M.

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), pp. 1–3 (2017).

Dimitropoulos, D.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

Eftekhar, A. A.

M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
[Crossref]

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

Georgas, M.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20(11), 12222–12232 (2012).
[Crossref]

Hosseini, E. S.

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014).
[Crossref]

Jalali, B.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Johnson, T. J.

Joshi, A.

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

Kippenberg, T. J.

Krishnamoorthy, A. V.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

Kumar, R.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

Kwon, Y. J.

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

Leu, J.

Levy, J. S.

K. Preston, N. Sherwood-Droz, J. S. Levy, and M. Lipson, “Performance guidelines for WDM interconnects based on silicon microring resonators,” in CLEO: 2011 - Laser Science to Photonic Applications, pp. 1–2 (2011).

Li, G.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

Li, H.

Li, Q.

M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
[Crossref]

Lin, S.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

Lipson, M.

J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16(21), 16659–16669 (2008).
[Crossref]

Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31(3), 341–343 (2006).
[Crossref]

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

V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004).
[Crossref]

K. Preston, N. Sherwood-Droz, J. S. Levy, and M. Lipson, “Performance guidelines for WDM interconnects based on silicon microring resonators,” in CLEO: 2011 - Laser Science to Photonic Applications, pp. 1–2 (2011).

Luo, Y.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

Miller, D. A. B.

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
[Crossref]

Moss, B.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20(11), 12222–12232 (2012).
[Crossref]

Ng, K. K.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (John Wiley & Sons Ltd., 2006).

Orcutt, J. S.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20(11), 12222–12232 (2012).
[Crossref]

Painter, O.

Pavanello, F.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

Popovic, M.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20(11), 12222–12232 (2012).
[Crossref]

M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), pp. 1–3 (2017).

Pradhan, S.

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

Preston, K.

J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16(21), 16659–16669 (2008).
[Crossref]

K. Preston, N. Sherwood-Droz, J. S. Levy, and M. Lipson, “Performance guidelines for WDM interconnects based on silicon microring resonators,” in CLEO: 2011 - Laser Science to Photonic Applications, pp. 1–2 (2011).

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

Raj, K.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

Ram, R. J.

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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
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M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
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J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20(11), 12222–12232 (2012).
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C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
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E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014).
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G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
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M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
[Crossref]

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Zheng, X.

G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
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[Crossref]

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[Crossref]

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G. Treyz, “Silicon Mach-Zehnder waveguide interferometers operating at 1.3 $\mu$μm,” Electron. Lett. 27(2), 118–120 (1991).
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G. Li, , A. V. Krishnamoorthy, , I. Shubin, J. Yao, Y. Luo, H. Thacker, X. Zheng, K. Raj, and J. E. Cunningham, “Ring resonator modulators in silicon for interchip photonic links,” IEEE J. Sel. Top. Quantum Electron. 19(6), 95–113 (2013).
[Crossref]

IEEE J. Solid-State Circuits (1)

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. H. Atabaki, F. Pavanello, J. M. Shainline, J. S. Orcutt, R. J. Ram, M. Popović, and V. Stojanović, “A 45 nm CMOS-SOI monolithic photonics platform with bit-statistics-based resonant microring thermal tuning,” IEEE J. Solid-State Circuits 51(4), 893–907 (2016).
[Crossref]

Nat. Commun. (1)

E. Timurdogan, C. M. Sorace-Agaskar, J. Sun, E. S. Hosseini, A. Biberman, and M. R. Watts, “An ultralow power athermal silicon modulator,” Nat. Commun. 5(1), 4008 (2014).
[Crossref]

Nature (1)

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (1)

M. Soltani, S. Yegnanarayanan, Q. Li, A. A. Eftekhar, and A. Adibi, “Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$Q photonic microresonators,” Phys. Rev. A 85(5), 053819 (2012).
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M. de Cea, A. H. Atabaki, L. Alloatti, M. Wade, M. Popovic, and R. J. Ram, “A thin silicon photonic platform for telecommunication wavelengths,” in 2017 European Conference on Optical Communication (ECOC), pp. 1–3 (2017).

K. Preston, N. Sherwood-Droz, J. S. Levy, and M. Lipson, “Performance guidelines for WDM interconnects based on silicon microring resonators,” in CLEO: 2011 - Laser Science to Photonic Applications, pp. 1–2 (2011).

A. Joshi, C. Batten, Y. J. Kwon, S. Beamer, I. Shamim, K. Asanovic, and V. Stojanovic, “Silicon-photonic clos networks for global on-chip communication,” in 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp. 124–133 (2009).

G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 2011).

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Figures (5)

Fig. 1.
Fig. 1. (a) Top view of the modeled resonant modulator. $S_{in}(t)$ and $S_{out}(t)$ represent the input and output optical E-fields, and $U(t)$ is the energy stored in the microring. $V(t)$ is the modulator’s driving signal. (b) Optical micrograph of the ring resonator used in the experiments. (c) Diagram of the physical phenomena occurring in a silicon optical device in the presence of two photon absorption (TPA). (d) Diagram of nonlinear effects in a silicon ring modulator and their inter-dependence. The modulation signal ($V(t)$) changes the resonance frequency ($\Delta W_0$) of the device, affecting the total stored energy in the resonator and setting the strength of TPA. TPA, in turn, modifies the resonance through two effects: free-carrier dispersion and self-heating. These two phenomena compete in opposite directions: free carrier dispersion shifts the resonance to shorter wavelengths, while heating pushes it to longer wavelengths.
Fig. 2.
Fig. 2. Device initialization. (a) Bistability curve of the microring extracted using the model in [23] for a 0.45 mW input power. $\lambda _0$ is the resonance wavelength of the ring and $\lambda$ is the laser wavelength. (b) Transmission as a function of wavelength for a 0.45 mW input optical power obtained with the model presented in this work. Red curve corresponds to the laser being abruptly turned on at a fixed wavelength, and the blue curve corresponds to the laser being swept from the blue side of the resonance and stopped at the target wavelength. The ER achievable when the laser is swept is considerably higher.
Fig. 3.
Fig. 3. Device optimum operational point. Theoretical (a) and experimental (b) evolution of the ER (black), IL (red) and normalized OMA (blue) as a function of laser wavelength for a 0.45 mW input power. Theoretical (c) and experimental (d) maximum attainable OMA (blue, left axis) and wavelength at which this value is reached (red, right axis) as a function of input power. The dashed line shows the expected evolution of OMA if no nonlinearities were present. Reported experimental powers are at the center laser wavelength and do not account for the extra input power due to unfiltered ASE optical power coming from the EDFA. The data rate used is 0.5 Gbps.
Fig. 4.
Fig. 4. Effects of nonlinearities in time domain. Simulated normalized output optical power as a function of time (blue, left axis) and resonance frequency shift due to temperature (red, right axis) and carrier density (green, right axis) fluctuations for 0.3 mW input optical power (a) and for 2 mW input optical power (c). Resonance shifts are referenced to the minimum shift for the operational condition being considered, so that the shown curves are $\Delta W_X(t)-min \left \{ \Delta W_X(t)\right \}$, where X refers to either temperature or carrier dispersion. Experimental normalized output optical power as a function of time for 0.1 mW input optical power (b) and for the experimental optimal input optical power of 1.65 mW (d). Reported experimental powers are at the center laser wavelength and do not account for extra input power due to unfiltered ASE optical power coming from the EDFA. The data rate is 0.5 Gbps. Reported temperature and carrier averages and standard deviations are calculated over a 2 $\mu s$ time series.
Fig. 5.
Fig. 5. Optimal operation point for high input optical powers. (a) Maximum attainable OMA (blue, left axis) and wavelength at which this value is reached (red, right axis) as a function of input power derived with the model. The dashed line shows the expected performance if no nonlinearities were present. (b)(c) Output optical power as a function of time (blue, left axis) and resonance frequency shift due to temperature (red, right axis) and carrier density (green, right axis) fluctuations for 5 mW of input optical power at the optimal operation wavelength of 1546.32 nm (b) and with a wavelength of 1547.52 nm, closer to the resonance (c). Resonance shifts are referenced to the minimum shift for the operational condition being considered, so that the shown curves are $\Delta W_X(t)-min \left \{ \Delta W_X(t)\right \}$, where X refers to either temperature or carrier dispersion. Reported temperature and carrier averages and standard deviations are calculated over a 2 $\mu s$ time series.

Tables (1)

Tables Icon

Table 1. Model parameters corresponding to the silicon microring modulator studied in this work. FEM = Finite Elements Method [13,14,15].

Equations (3)

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Δ W 0 ( t ) W 0 = 1 n S i ( d n S i d T Δ T ( t ) ¯ + ( d n S i d N p + d n S i d N n ) N ( t ) ¯ ) + Δ W 0 m o d ( t ) W 0
Δ W 0 m o d ( t ) = d W 0 d V p n V p n ( t )
d V p n ( t ) d t = V p n ( t ) τ + V ( t ) τ