Abstract

We propose an on-chip triply resonant electro-optic modulator architecture for RF-to-optical signal conversion and provide a detailed theoretical analysis of the optimal “circuit-level” device geometries and their performance limits. The designs maximize the RF-optical conversion efficiency through simultaneous resonant enhancement of the RF drive signal, a continuous-wave (CW) optical pump, and the generated optical sideband. The optical pump and sideband are resonantly enhanced in respective supermodes of a two-coupled-cavity optical resonator system, while the RF signal can be enhanced in addition by an LC circuit formed by capacitances of the optical resonator active regions and (integrated) matching inductors. We show that such designs can offer 15-50 dB improvement in conversion efficiency over conventional microring modulators. In the proposed configurations, the photon lifetime (resonance linewidth) limits the instantaneous RF bandwidth of the electro-optic response but does not limit its central RF frequency. The latter is set by the coupling strength between the two coupled cavities and is not subject to the photon lifetime constraint inherent to conventional singly resonant microring modulators. This feature enables efficient operation at high RF carrier frequencies without a reduction in efficiency commonly associated with the photon lifetime limit and accounts for 10-30 dB of the total improvement. Two optical configurations of the modulator are proposed: a “basic” configuration with equal Q-factors in both supermodes, most suitable for narrowband RF signals, and a “generalized” configuration with independently tailored supermode Q-factors that supports a wider instantaneous bandwidth. A second significant 5-20 dB gain in modulation efficiency is expected from RF drive signal enhancement by integrated LC resonant matching, leading to the total expected improvement of 15-50 dB. Previously studied triply-resonant modulators, with coupled longitudinal (across the free spectral range (FSR)) modes, have large resonant mode volume for typical RF frequencies, which limits the interaction between the optical and RF fields. In contrast, the proposed modulators support maximally tightly confined resonant modes, with strong coupling between the mode fields, which increases and maintains high device efficiency across a range of RF frequencies. The proposed modulator architecture is compact, efficient, capable of modulation at high RF carrier frequencies and can be applied to any cavity design or modulation mechanism. It is also well suited to moderate Q, including silicon, implementations, and may be enabling for future CMOS RF-electronic-photonic systems on chip.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

K. Giewont, K. Nummy, F. A. Anderson, J. Ayala, T. Barwicz, Y. Bian, K. K. Dezfulian, D. M. Gill, T. Houghton, S. Hu, B. Peng, M. Rakowski, S. Rauch, J. C. Rosenberg, A. Sahin, I. Stobert, and A. Stricker, “300-mm Monolithic Silicon Photonics Foundry Technology,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–11 (2019).
[Crossref]

2018 (4)

2017 (4)

C. Hoessbacher, A. Josten, B. Baeuerle, Y. Fedoryshyn, H. Hettrich, Y. Salamin, W. Heni, C. Haffner, C. Kaiser, R. Schmid, D. L. Elder, D. Hillerkuss, M. Möller, L. R. Dalton, and J. Leuthold, “Plasmonic modulator with >170 GHz bandwidth demonstrated at 100 GBd NRZ,” Opt. Express 25(3), 1762 (2017).
[Crossref]

S. Moazeni, S. Lin, M. Wade, L. Alloatti, R. J. Ram, M. A. Popović, and V. Stojanović, “A 40-Gb/s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS,” IEEE J. Solid-State Circuits 52(12), 3503–3516 (2017).
[Crossref]

M. Pantouvaki, S. A. Srinivasan, Y. Ban, P. D. Heyn, P. Verheyen, G. Lepage, H. Chen, J. D. Coster, N. Golshani, S. Balakrishnan, P. Absil, and J. V. Campenhout, “Active Components for 50 Gb/s NRZ-OOK Optical Interconnects in a Silicon Photonics Platform,” J. Lightwave Technol. 35(4), 631–638 (2017).
[Crossref]

M. Soltani, M. Zhang, C. Ryan, G. J. Ribeill, C. Wang, and M. Loncar, “Efficient quantum microwave-to-optical conversion using electro-optic nanophotonic coupled resonators,” Phys. Rev. A 96(4), 043808 (2017).
[Crossref]

2015 (4)

2014 (4)

2013 (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
[Crossref]

2010 (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. Microwave Theory Tech. 58(11), 3167–3174 (2010).
[Crossref]

2008 (1)

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

2006 (1)

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Tech. 54(2), 832–846 (2006).
[Crossref]

2005 (2)

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

T. O. Dickson, M. A. LaCroix, S. Boret, D. Gloria, R. Beerkens, and S. P. Voinigescu, “30-100-GHz inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits,” IEEE Trans. Microwave Theory Tech. 53(1), 123–133 (2005).
[Crossref]

2003 (1)

2002 (1)

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[Crossref]

2001 (2)

D. A. Cohen, M. Hossein-Zadeh, and A. F. Levi, “High-Q microphotonic electro-optic modulator,” Solid-State Electron. 45(9), 1577–1589 (2001).
[Crossref]

R. C. Williamson, “Sensitivity-bandwidth product for electro-optic modulators,” Opt. Lett. 26(17), 1362 (2001).
[Crossref]

1998 (1)

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Abel, S.

F. Eltes, M. Kroh, D. Caimi, C. Mai, Y. Popoff, G. Winzer, D. Petousi, S. Lischke, J. E. Ortmann, L. Czornomaz, L. Zimmermann, J. Fompeyrine, and S. Abel, “A novel 25 Gbps electro-optic Pockels modulator integrated on an advanced Si photonic platform,” in International Electron Devices Meeting, (IEEE, 2017), pp. 24.5.1–24.5.4.

Absil, P.

Alexander, K.

K. Alexander, J. P. George, B. Kuyken, J. Beeckman, and D. Van Thourhout, “Broadband Electro-optic Modulation using Low-loss PZT-on-Silicon Nitride Integrated Waveguides,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), paper JTh5C.7.

Alloatti, L.

V. Stojanović, R. J. Ram, M. Popović, S. Lin, S. Moazeni, M. Wade, C. Sun, L. Alloatti, A. Atabaki, F. Pavanello, N. Mehta, and P. Bhargava, “Monolithic silicon-photonic platforms in state-of-the-art CMOS SOI processes [Invited],” Opt. Express 26(10), 13106 (2018).
[Crossref]

S. Moazeni, S. Lin, M. Wade, L. Alloatti, R. J. Ram, M. A. Popović, and V. Stojanović, “A 40-Gb/s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS,” IEEE J. Solid-State Circuits 52(12), 3503–3516 (2017).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Anderson, F. A.

K. Giewont, K. Nummy, F. A. Anderson, J. Ayala, T. Barwicz, Y. Bian, K. K. Dezfulian, D. M. Gill, T. Houghton, S. Hu, B. Peng, M. Rakowski, S. Rauch, J. C. Rosenberg, A. Sahin, I. Stobert, and A. Stricker, “300-mm Monolithic Silicon Photonics Foundry Technology,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–11 (2019).
[Crossref]

Ardalan, S.

R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Atabaki, A.

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Ayala, J.

K. Giewont, K. Nummy, F. A. Anderson, J. Ayala, T. Barwicz, Y. Bian, K. K. Dezfulian, D. M. Gill, T. Houghton, S. Hu, B. Peng, M. Rakowski, S. Rauch, J. C. Rosenberg, A. Sahin, I. Stobert, and A. Stricker, “300-mm Monolithic Silicon Photonics Foundry Technology,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–11 (2019).
[Crossref]

Baehr-Jones, T.

Baeuerle, B.

Bahrami, H.

Z. Yong, W. D. Sacher, Y. Huang, J. C. Mikkelsen, Y. Yang, X. Luo, P. Dumais, D. Goodwill, H. Bahrami, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Efficient Single-Drive Push-Pull Silicon Mach-Zehnder Modulators with U-Shaped PN Junctions for the O-Band,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Tu2H.2.

Balakrishnan, S.

Ban, Y.

Barwicz, T.

K. Giewont, K. Nummy, F. A. Anderson, J. Ayala, T. Barwicz, Y. Bian, K. K. Dezfulian, D. M. Gill, T. Houghton, S. Hu, B. Peng, M. Rakowski, S. Rauch, J. C. Rosenberg, A. Sahin, I. Stobert, and A. Stricker, “300-mm Monolithic Silicon Photonics Foundry Technology,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–11 (2019).
[Crossref]

Beeckman, J.

K. Alexander, J. P. George, B. Kuyken, J. Beeckman, and D. Van Thourhout, “Broadband Electro-optic Modulation using Low-loss PZT-on-Silicon Nitride Integrated Waveguides,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), paper JTh5C.7.

Beerkens, R.

T. O. Dickson, M. A. LaCroix, S. Boret, D. Gloria, R. Beerkens, and S. P. Voinigescu, “30-100-GHz inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits,” IEEE Trans. Microwave Theory Tech. 53(1), 123–133 (2005).
[Crossref]

Bergman, K.

Bernier, E.

Z. Yong, W. D. Sacher, Y. Huang, J. C. Mikkelsen, Y. Yang, X. Luo, P. Dumais, D. Goodwill, H. Bahrami, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Efficient Single-Drive Push-Pull Silicon Mach-Zehnder Modulators with U-Shaped PN Junctions for the O-Band,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Tu2H.2.

Bhargava, P.

Bian, Y.

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T. Pett, J. Lee, Y. Ehrlichman, H. Gevorgyan, A. Khilo, and M. A. Popović, “Photonics-based Microwave Radiometer for Hyperspectral Earth Remote Sensing,” in Proceedings of IEEE International Topical Meeting on Microwave Photonics, (IEEE, 2018).

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Schmidt, B.

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V. Stojanović, R. J. Ram, M. Popović, S. Lin, S. Moazeni, M. Wade, C. Sun, L. Alloatti, A. Atabaki, F. Pavanello, N. Mehta, and P. Bhargava, “Monolithic silicon-photonic platforms in state-of-the-art CMOS SOI processes [Invited],” Opt. Express 26(10), 13106 (2018).
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S. Moazeni, S. Lin, M. Wade, L. Alloatti, R. J. Ram, M. A. Popović, and V. Stojanović, “A 40-Gb/s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS,” IEEE J. Solid-State Circuits 52(12), 3503–3516 (2017).
[Crossref]

Stojanovic, V. M.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Stricker, A.

K. Giewont, K. Nummy, F. A. Anderson, J. Ayala, T. Barwicz, Y. Bian, K. K. Dezfulian, D. M. Gill, T. Houghton, S. Hu, B. Peng, M. Rakowski, S. Rauch, J. C. Rosenberg, A. Sahin, I. Stobert, and A. Stricker, “300-mm Monolithic Silicon Photonics Foundry Technology,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–11 (2019).
[Crossref]

Sun, C.

V. Stojanović, R. J. Ram, M. Popović, S. Lin, S. Moazeni, M. Wade, C. Sun, L. Alloatti, A. Atabaki, F. Pavanello, N. Mehta, and P. Bhargava, “Monolithic silicon-photonic platforms in state-of-the-art CMOS SOI processes [Invited],” Opt. Express 26(10), 13106 (2018).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

Sun, J.

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

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H. Jiang, J. Yeh, Y. Wang, and N. Tien, “Electromagnetically shielded high-Q CMOS-compatible copper inductors,” in International Solid-State Circuits Conference, (IEEE, 2000), pp. 330–331.

Timurdogan, E.

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

Tzuang, L. D.

Van Campenhout, J.

H. Yu, M. Pantouvaki, P. Verheyen, G. Lepage, P. Absil, W. Bogaerts, and J. Van Campenhout, “Silicon dual-ring modulator driven by differential signal,” Opt. Lett. 39(22), 6379–6382 (2014).
[Crossref]

M. Pantouvaki, P. Verheyen, J. De Coster, G. Lepage, P. Absil, and J. Van Campenhout, “56Gb/s ring modulator on a 300mm silicon photonics platform,” in European Conference on Optical Communication, (IEEE, 2015), pp. 1–3.

Van Thourhout, D.

K. Alexander, J. P. George, B. Kuyken, J. Beeckman, and D. Van Thourhout, “Broadband Electro-optic Modulation using Low-loss PZT-on-Silicon Nitride Integrated Waveguides,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), paper JTh5C.7.

Veerasubramanian, V.

Verheyen, P.

Voinigescu, S. P.

T. O. Dickson, M. A. LaCroix, S. Boret, D. Gloria, R. Beerkens, and S. P. Voinigescu, “30-100-GHz inductors and transformers for millimeter-wave (Bi)CMOS integrated circuits,” IEEE Trans. Microwave Theory Tech. 53(1), 123–133 (2005).
[Crossref]

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V. Stojanović, R. J. Ram, M. Popović, S. Lin, S. Moazeni, M. Wade, C. Sun, L. Alloatti, A. Atabaki, F. Pavanello, N. Mehta, and P. Bhargava, “Monolithic silicon-photonic platforms in state-of-the-art CMOS SOI processes [Invited],” Opt. Express 26(10), 13106 (2018).
[Crossref]

S. Moazeni, S. Lin, M. Wade, L. Alloatti, R. J. Ram, M. A. Popović, and V. Stojanović, “A 40-Gb/s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS,” IEEE J. Solid-State Circuits 52(12), 3503–3516 (2017).
[Crossref]

R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

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M. T. Wade, X. Zeng, and M. A. Popović, “Wavelength conversion in modulated coupled-resonator systems and their design via an equivalent linear filter representation,” Opt. Lett. 40(1), 107–110 (2015).
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C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

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S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS Technology,” in International Electron Devices Meeting, (IEEE, 2007), pp. 255–258.

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C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547 (2018).
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M. Soltani, M. Zhang, C. Ryan, G. J. Ribeill, C. Wang, and M. Loncar, “Efficient quantum microwave-to-optical conversion using electro-optic nanophotonic coupled resonators,” Phys. Rev. A 96(4), 043808 (2017).
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M. Zhang, C. Wang, Y. Hu, A. Shams-Ansari, G. Ribeill, M. Soltani, and M. Loncar, “Microwave-to-Optical Converter based on Integrated Lithium Niobite Coupled-Resonators,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), paper SM1I.7.

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H. Jiang, J. Yeh, Y. Wang, and N. Tien, “Electromagnetically shielded high-Q CMOS-compatible copper inductors,” in International Solid-State Circuits Conference, (IEEE, 2000), pp. 330–331.

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C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Watts, M. R.

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

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S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS Technology,” in International Electron Devices Meeting, (IEEE, 2007), pp. 255–258.

Williamson, R. C.

Winzer, G.

F. Eltes, M. Kroh, D. Caimi, C. Mai, Y. Popoff, G. Winzer, D. Petousi, S. Lischke, J. E. Ortmann, L. Czornomaz, L. Zimmermann, J. Fompeyrine, and S. Abel, “A novel 25 Gbps electro-optic Pockels modulator integrated on an advanced Si photonic platform,” in International Electron Devices Meeting, (IEEE, 2017), pp. 24.5.1–24.5.4.

Wolf, S.

Wright-Gladstein, A.

R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

Xu, Q.

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

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R. Ding, Y. Liu, Y. Ma, Y. Yang, Q. Li, A. E. J. Lim, G. Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “High-speed silicon modulator with slow-wave electrodes and fully independent differential drive,” J. Lightwave Technol. 32(12), 2240–2247 (2014).
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Z. Yong, W. D. Sacher, Y. Huang, J. C. Mikkelsen, Y. Yang, X. Luo, P. Dumais, D. Goodwill, H. Bahrami, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Efficient Single-Drive Push-Pull Silicon Mach-Zehnder Modulators with U-Shaped PN Junctions for the O-Band,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Tu2H.2.

Yeh, J.

H. Jiang, J. Yeh, Y. Wang, and N. Tien, “Electromagnetically shielded high-Q CMOS-compatible copper inductors,” in International Solid-State Circuits Conference, (IEEE, 2000), pp. 330–331.

Yong, Z.

Z. Yong, W. D. Sacher, Y. Huang, J. C. Mikkelsen, Y. Yang, X. Luo, P. Dumais, D. Goodwill, H. Bahrami, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Efficient Single-Drive Push-Pull Silicon Mach-Zehnder Modulators with U-Shaped PN Junctions for the O-Band,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Tu2H.2.

Yu, H.

Zamdmer, N.

S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS Technology,” in International Electron Devices Meeting, (IEEE, 2007), pp. 255–258.

Zeng, X.

Zhang, C.

R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

Zhang, M.

C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547 (2018).
[Crossref]

M. Soltani, M. Zhang, C. Ryan, G. J. Ribeill, C. Wang, and M. Loncar, “Efficient quantum microwave-to-optical conversion using electro-optic nanophotonic coupled resonators,” Phys. Rev. A 96(4), 043808 (2017).
[Crossref]

M. Zhang, C. Wang, Y. Hu, A. Shams-Ansari, G. Ribeill, M. Soltani, and M. Loncar, “Microwave-to-Optical Converter based on Integrated Lithium Niobite Coupled-Resonators,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), paper SM1I.7.

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F. Eltes, M. Kroh, D. Caimi, C. Mai, Y. Popoff, G. Winzer, D. Petousi, S. Lischke, J. E. Ortmann, L. Czornomaz, L. Zimmermann, J. Fompeyrine, and S. Abel, “A novel 25 Gbps electro-optic Pockels modulator integrated on an advanced Si photonic platform,” in International Electron Devices Meeting, (IEEE, 2017), pp. 24.5.1–24.5.4.

Zwickel, H.

IEEE J. Sel. Top. Quantum Electron. (1)

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IEEE J. Solid-State Circuits (1)

S. Moazeni, S. Lin, M. Wade, L. Alloatti, R. J. Ram, M. A. Popović, and V. Stojanović, “A 40-Gb/s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS,” IEEE J. Solid-State Circuits 52(12), 3503–3516 (2017).
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Nature (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
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C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
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Phys. Rev. A (1)

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R. Meade, S. Ardalan, M. Davenport, J. Fini, C. Sun, M. Wade, A. Wright-Gladstein, and C. Zhang, “TeraPHY: A High-density Electronic-Photonic Chiplet for Optical I/O from a Multi-Chip Module,” in Optical Fiber Communication Conference (OFC) 2019, (Optical Society of America, 2019), paper M4D.7.

H. Jiang, J. Yeh, Y. Wang, and N. Tien, “Electromagnetically shielded high-Q CMOS-compatible copper inductors,” in International Solid-State Circuits Conference, (IEEE, 2000), pp. 330–331.

K. Alexander, J. P. George, B. Kuyken, J. Beeckman, and D. Van Thourhout, “Broadband Electro-optic Modulation using Low-loss PZT-on-Silicon Nitride Integrated Waveguides,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2017), paper JTh5C.7.

M. Pantouvaki, P. Verheyen, J. De Coster, G. Lepage, P. Absil, and J. Van Campenhout, “56Gb/s ring modulator on a 300mm silicon photonics platform,” in European Conference on Optical Communication, (IEEE, 2015), pp. 1–3.

F. Eltes, M. Kroh, D. Caimi, C. Mai, Y. Popoff, G. Winzer, D. Petousi, S. Lischke, J. E. Ortmann, L. Czornomaz, L. Zimmermann, J. Fompeyrine, and S. Abel, “A novel 25 Gbps electro-optic Pockels modulator integrated on an advanced Si photonic platform,” in International Electron Devices Meeting, (IEEE, 2017), pp. 24.5.1–24.5.4.

Z. Yong, W. D. Sacher, Y. Huang, J. C. Mikkelsen, Y. Yang, X. Luo, P. Dumais, D. Goodwill, H. Bahrami, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Efficient Single-Drive Push-Pull Silicon Mach-Zehnder Modulators with U-Shaped PN Junctions for the O-Band,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Tu2H.2.

S. Lee, B. Jagannathan, S. Narasimha, A. Chou, N. Zamdmer, J. Johnson, R. Williams, L. Wagner, J. Kim, J.-O. Plouchart, J. Pekarik, S. Springer, and G. Freeman, “Record RF performance of 45-nm SOI CMOS Technology,” in International Electron Devices Meeting, (IEEE, 2007), pp. 255–258.

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Figures (7)

Fig. 1.
Fig. 1. (a) Conceptual representation of the triply resonant modulator, consisting of one RF and two optical mutually coupled resonances at frequencies of the three interacting waves: the input RF drive, the input laser pump, and the output optical sideband. (b,c) Physical realization of the two optical resonances by supermodes of (b) the basic coupled-cavity design, with a conventional bus waveguide, and (c) the generalized coupled-cavity design, with novel interferometrically coupled input/output waveguides. (d) Non-resonant RF design, where the transmission line directly feeds the active optical cavities. Due to impedance mismatch between them, RF power is almost completely reflected from the load. (e) Resonant design, where the RF resonance from (a) is realized by LC circuits, consisting of integrated inductors $L_1$ and capacitances $C_m$ of the active cavities. It greatly reduces RF power reflection and enhances the voltage on the active cavities. (f) Resonant-matched design, where critical coupling between the transmission line and the RF resonator is achieved using impedance matching circuits which consist of inductors $L_2$ and capacitors $C_2$ . The plots at the bottom of (d)-(f) sketch the frequency dependence of the power reflection $\lvert \Gamma \rvert ^2$ of the RF signal back into the transmission line.
Fig. 2.
Fig. 2. Resonant modulators for RF-to-optical conversion (a,b) previously demonstrated and (c,d) studied in this work. (a) Regular microring modulators are compact and efficient, but suffer from the efficiency-frequency range tradeoff. (b) Millimeter-scale disk or ring resonator modulators, which overcome the efficiency-frequency range tradeoff through modulation-induced coupling between multiple resonant mode orders at adjacent FSRs, have large footprint and require implementation of RF traveling-wave electrodes. (c,d) Optical coupled-cavity designs of the proposed modulator perform RF-to-optical conversion by transferring optical energy from the symmetric to the antisymmetric supermode resonance, via push-pull modulation of the resonance frequencies of the coupled microresonators. The designs are compact, efficient and do not suffer from the efficiency-frequency range tradeoff. Additionally, unlike the basic proposed design, where supermodes have equal Q-factors, (d) the generalized design allows independent tailoring of supermode Q-factors, providing higher efficiency with larger modulation bandwidth if the symmetric resonance is kept at critical coupling and the antisymmetric resonance is broadened just enough to accommodate the RF spectrum.
Fig. 3.
Fig. 3. Graphical representation of the parameters in conversion efficiency formula (2), with decay rates $r_o$ and $r_{e,s}$ ( $r_{e,a}$ ) determining the linewidth of the symmetric (antisymmetric) supermode resonance, shown by light (dark) blue dashed line, coupling rate $\mu$ determining the frequency splitting between the supermode resonances, RF frequency $\Omega$ setting the separation between the laser pump (light blue arrow) and the optical sideband (dark blue arrow), and $\Delta \omega _s$ ( $\Delta \omega _a$ ) representing the detuning of the laser pump (optical sideband) from the symmetric (antisymmetric) resonance. The relationship between $\mu$ , $\Omega$ , $\Delta \omega _s$ and $\Delta \omega _a$ is given by Eq. (3).
Fig. 4.
Fig. 4. (a) Peak conversion efficiency versus resonance frequency swing $\delta \omega _m$ , where $r_{e,s}$ and $r_{e,a}$ are optimized according to Eq. (4) either at each point along the x-axis (solid blue line), or for each of several values of resonance frequency swing $\delta \omega _m^{opt}$ (dashed lines). (b) Small-signal conversion efficiencies of the proposed and the regular microring modulators versus RF carrier frequency, where the modulators are optimized for maximum efficiency at each point along x-axis. (c) RF-to-optical conversion frequency response of the modulator, optimized for maximum conversion at $\Omega = \Omega _o$ , for several values of $\delta \omega _m$ . (d) Photon-lifetime-limited RF bandwidth, defined as full width at half maximum of the magnitude response, versus resonance frequency swing $\delta \omega _m$ .
Fig. 5.
Fig. 5. (a,b) Design external decay rates $r_{e,s}$ and $r_{e,a}$ versus RF bandwidth $\Delta \Omega _{3dB}$ for (a) the basic and (b) the generalized designs, optimized for maximum conversion efficiency. (c,d) Peak conversion efficiency versus $\Delta \Omega _{3dB}$ and $\delta \omega _m$ for (c) the basic and (d) the generalized designs. (e) The improvement in conversion efficiency that the generalized design provides over the basic design versus $\Delta \Omega _{3dB}$ and $\delta \omega _m$ .
Fig. 6.
Fig. 6. RF configurations of the proposed modulator with (a) non-resonant, (b) resonant, (c) resonant-matched designs on the left and corresponding equivalent circuits on the right.
Fig. 7.
Fig. 7. (a) Magnitude response of the non-resonant circuit of Fig. 6(a) (solid blue line) and of the resonant circuit of Fig. 6(b) for RF resonance frequency $\Omega _o$ equal to 1, 10, and 100 GHz (dashed lines). (b) The gain in conversion efficiency the resonant design provides compared to the non-resonant design versus $\Omega _o$ for several values of $Q_L$ of the integrated inductor. Values of $C_m$ =5 fF, $R_m$ =100 Ohm, $Z_o$ =50 Ohm are assumed for the plots in (a) and (b). (c) The additional gain in conversion efficiency the resonant-matched circuit provides compared to resonant design versus normalized parasitic resistance of the active cavities.

Tables (1)

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Table 1. List of symbols and their descriptions.

Equations (34)

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G = P s i d e b a n d P p u m p .
G = 1 4 r e , s r e , a δ ω m 2 [ ( r o + r e , a ) Δ ω s + ( r o + r e , s ) Δ ω a ] 2 + [ ( r o + r e , s ) ( r o + r e , a ) + ( δ ω m 4 ) 2 Δ ω s Δ ω a ] 2
Δ ω a Δ ω s = Ω 2 μ .
r e , s = r e , a = r o 2 + ( δ ω m 4 ) 2 .
G ( Ω o ) = ( δ ω m 4 1 2 r o ) 2 .
Δ Ω 3 d B = 4 r o 2 + ( δ ω m 4 ) 2 .
Δ Ω 3 d B = 2 ( r o + r e , a ) + 1 2 ( r o + r e , s ) ( δ ω m 2 ) 2 .
r e , s = r e , a = Δ Ω 3 d B 4 r o + ( Δ Ω 3 d B 4 ) 2 ( δ ω m 4 ) 2 , and Δ Ω 3 d B m i n = { 2 r o + 1 2 r o ( δ ω m 2 ) 2 , if  δ ω m 4 r o δ ω m   , if  δ ω m > 4 r o
r e , s = 1 8 ( Δ Ω 3 d B 2 r o ) [ δ ω m 2 + [ δ ω m 2 8 r o ( Δ Ω 3 d B 2 r o ) ] 2 + 8 r o δ ω m 2 ( Δ Ω 3 d B 2 r o ) ] , r e , a = Δ Ω 3 d B 2 r o 3 1 48 r o [ δ ω m 2 [ δ ω m 2 8 r o ( Δ Ω 3 d B 2 r o ) ] 2 + 8 r o δ ω m 2 ( Δ Ω 3 d B 2 r o ) ] , and Δ Ω 3 d B m i n = 2 r o .
r e , s = r e , a 1 2 Δ Ω 3 d B r o (basic) , r e , s r o , r e , a 1 2 Δ Ω 3 d B r o (generalized) .
δ ω m = 2 π c V C m n g V π L = 2 π c n g V π L | H ( Ω ) | 2 Z o P R F   ,
H R C ( Ω ) V C m V R F = 2 1 + j Ω ( Z o + R m ) C m .
H R L C = V C m V s = 2 1 Ω 2 L 1 C m + j Ω ( Z o + R m + R L 1 ) C m .
G 1 ( Ω o ) = | H R L C H R C | Ω o 2 = ( Q R F t o t ) 2 [ 1 + ( 1 Q R F t o t 1 Q L ) 2 ] .
G 2 ( Ω o ) = | H R L C m a t c h H R C | Ω o 2 = 1 4 ( R m Z o + Z o R m ) 2 G 1 = G 21 G 1 ,
G ( Ω o ) = 2 Z o P R F ( 5 π l n ( 10 ) ) 2 ( Q R F t o t V π L α ) 2
F O M = Q R F t o t V π L α .
d d t a ¯ = j ω ¯ ¯ a ¯ j μ ¯ ¯ a ¯
a ¯ = ( a 1 a 2 ) , ω ¯ ¯ = ( ω o δ ω ( t ) + j r o 0 0 ω o + δ ω ( t ) + j r o ) , μ ¯ ¯ = ( 0 μ μ 0 ) .
( a 1 a 2 ) s , a = 1 2 ( 1 ± 1 ) ,
ω s , a = ω o μ + j r o .
d d t b ¯ = j ω ¯ ¯ b ¯ j μ ¯ ¯ b ¯
b ¯ = ( b 1 b 2 ) = 1 2 ( a 1 + a 2 a 1 a 2 ) ,
ω ¯ ¯ = ( ω o μ + j r o 0 0 ω o + μ + j r o ) , μ ¯ ¯ = ( 0 δ ω ( t ) δ ω ( t ) 0 ) .
d d t b ¯ = j ω ¯ ¯ b ¯ j μ ¯ ¯ b ¯ j M i ¯ ¯ s ¯ + s ¯ = j M o ¯ ¯ b ¯ + s ¯ +
ω ¯ ¯ = ( ω o μ + j ( r o + r e , s ) 0 0 ω o + μ + j ( r o + r e , a ) ) , μ ¯ ¯ = ( 0 δ ω ( t ) δ ω ( t ) 0 ) , M i ¯ ¯ = ( 2 r e , s 0 0 2 r e , a ) , M o ¯ ¯ = M i ¯ ¯ T , s ¯ + = ( s + 1 s + 2 ) , s ¯ = ( s 1 s 2 ) .
α = 20 n g r o l n ( 10 ) c , κ i n 2 = 2 r e , i n Δ f F S R , κ o u t 2 = 2 r e , o u t Δ f F S R , κ r r 2 = μ 2 Δ f F S R 2 ,
b 1 ( t ) B 1 ( t ) e j ( ω o μ ) t , b 2 ( t ) B 2 ( t ) e j ( ω o + μ ) t , s + 1 ( t ) S + 1 ( t ) e j ( ω o μ ) t
d d t B ¯ = j H ¯ ¯ B ¯ j M i ¯ ¯ S ¯ + S ¯ = j M o ¯ ¯ B ¯ + S ¯ +
B ¯ = ( B 1 B 2 ) , H ¯ ¯ = ( j ( r o + r e , s ) δ ω m 4 ( e j ( Ω + 2 μ ) t + e j ( Ω 2 μ ) t ) δ ω m 4 ( e j ( Ω 2 μ ) t + e j ( Ω + 2 μ ) t ) j ( r o + r e , a ) ) , S ¯ + = ( S + 1 S + 2 ) , S ¯ = ( S 1 S 2 ) ,
j Δ ω ¯ ¯ B ~ ¯ = j H ¯ ¯ B ~ ¯ j M i ¯ ¯ S ~ ¯ + S ~ ¯ = j M o ¯ ¯ B ~ ¯ + S ~ ¯ +
Δ ω ¯ ¯ = ( Δ ω s 0 0 Δ ω a ) , B ~ ¯ = ( B ~ 1 B ~ 2 ) , H ¯ ¯ = ( j ( r o + r e , s ) δ ω m 4 δ ω m 4 j ( r o + r e , a ) ) ,   S ~ ¯ + = ( S ~ + 1 S ~ + 2 ) ,   S ~ ¯ ( S ~ 1 S ~ 2 ) ,
  G = | S ~ 2 S ~ + 1 | 2 = = 1 4 r e , s r e , a δ ω m 2 [ ( r o + r e , a ) Δ ω s + ( r o + r e , s ) Δ ω a ] 2 + [ ( r o + r e , s ) ( r o + r e , a ) + ( δ ω m 4 ) 2 Δ ω s Δ ω a ] 2
G = ( δ ω m 4 1 2 r o ) 2 1 ( Δ ω s 2 r o r e , s ) 2 + 1 4 ( r o r e , s + r e , s r o ) 2 1 ( Δ ω a 2 r o r e , a ) 2 + 1 4 ( r o r e , a + r e , a r o ) 2 ,

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