Abstract

Future high-performance computers demand highly dynamic data rates, e.g., a few terabytes per second communication bandwidth between switch hubs, and hundreds of gigabytes per second bandwidth between nodes and hubs, in order to overcome the challenges to rapidly growing traffic. Integrated photonic interconnect on silicon is believed to be one of the best solutions for low-cost, energy efficient, and high-speed data communications because of its fundamental advantages in high-volume throughput and dense integration. Applied with signal multiplexing techniques, e.g., wavelength division multiplexing (WDM), large bandwidth data links have been proved to be achievable on silicon. In such a system, an on-chip, robust, low-power consumption laser source is the key component as well as one of the fundamental limits to the silicon platform. In this work, we report the first hybrid silicon microring lasers with quantum-dot (QD) gain material to show great potential for uncooled, highly energy efficient, and isolator-free operation. The hybrid silicon QD lasers have a microring cavity with a 50 μm diameter that incorporates InAs/GaAs QD gain material at a 1.3 μm emission wavelength. The threshold current is as low as 0.7 mA under continuous wave (CW) operation at room temperature, and the laser operates at stage temperatures of up to 70°C. We demonstrate, to the best of our knowledge, a hybrid QD laser with non-return-to-zero (NRZ) communication at a record-high direct modulation rate of 15 Gb/s with energy efficiency of 1.2 pJ/bit. We believe this work shows huge benefits from superior QD lasing material and hybrid photonic integration not only for data communications but also optical memory and many other emerging applications.

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

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References

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2018 (6)

L. Sanchez, F. Fournel, B. Montmayeul, L. Bally, B. Szelag, and L. Adelmini, “Collective die direct bonding for photonic on silicon,” Electrochem. Soc. Trans. 86, 223–231 (2018).
[Crossref]

G. Kurczveil, A. Seyedi, D. Liang, M. Fiorentino, and R. G. Beausoleil, “Error-free operation in a hybrid-silicon quantum dot comb laser,” Photon. Technol. Lett. 30, 71–74 (2018).
[Crossref]

D. Jung, R. Herrick, J. Norman, K. Turnlund, C. Jan, K. Feng, A. C. Gossard, and J. E. Bowers, “Impact of threading dislocation density on the lifetime of InAs quantum dot lasers on Si,” Appl. Phys. Lett. 112, 153507 (2018).
[Crossref]

S. Uvin, S. Kumari, A. De Groote, S. Verstuyft, G. Lepage, P. Verheyen, J. Van Campenhout, G. Morthier, D. Van Thourhout, and G. Roelkens, “1.3 μm InAs/GaAs quantum dot DFB laser integrated on a Si waveguide circuit by means of adhesive die-to-wafer bonding,” Opt. Express 26, 18302–18309 (2018).
[Crossref]

P. O. Weigel, J. Zhao, K. Fang, H. Al-Rubaye, D. Trotter, D. Hood, J. Mudrick, C. Dallo, A. T. Pomerene, A. L. Starbuck, C. T. DeRose, A. L. Lentine, G. Rebeiz, and S. Mookherjea, “Bonded thin film lithium niobate modulator on a silicon photonics platform exceeding 100  GHz 3  dB electrical modulation bandwidth,” Opt. Express 26, 23728–23739 (2018).
[Crossref]

H. Huang, J. Duan, D. Jung, A. Y. Liu, Z. Zhang, J. Norman, J. E. Bowers, and F. Grillot, “Analysis of the optical feedback dynamics in InAs/GaAs quantum dot lasers directly grown on silicon,” J. Opt. Soc. Am. B 35, 2780–2787 (2018).
[Crossref]

2017 (1)

T. Hiraki, T. Aihara, K. Hasebe, K. Takeda, T. Fujii, T. Kakitsuka, T. Tsuchizawa, H. Fukuda, and S. Matsuo, “Heterogeneously integrated III–V/Si MOS capacitor Mach–Zehnder modulator,” Nat. Photonics 11, 482–485 (2017).
[Crossref]

2016 (8)

D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Electrically driven and thermally tunable integrated optical isolators for silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 22, 271–278 (2016).
[Crossref]

T. Komljenovic, M. Davenport, J. Hulme, A. Y. Liu, C. T. Santis, A. Spott, S. Srinivasan, E. J. Stanton, C. Zhang, and J. E. Bowers, “Heterogeneous silicon photonic integrated circuits,” J. Lightwave Technol. 34, 20–35 (2016).
[Crossref]

G. Kurczveil, D. Liang, M. Fiorentino, and R. G. Beausoleil, “Robust hybrid quantum dot laser for integrated silicon photonics,” Opt. Express 24, 16167–16174 (2016).
[Crossref]

C. Zhang, S. Zhang, J. D. Peters, and J. E. Bowers, “8×8×40  Gbps fully integrated silicon photonic network on chip,” Optica 3, 785–786 (2016).
[Crossref]

Y.-H. Jhang, R. Mochida, K. Tanabe, K. Takemasa, M. Sugawara, S. Iwamoto, and Y. Arakawa, “Direct modulation of 1.3  μm quantum dot lasers on silicon at 60 °C,” Opt. Express 24, 18428–18435 (2016).
[Crossref]

S. Chen, W. Li, J. Wu, Q. Jiang, M. Tang, S. Shutts, S. N. Elliott, A. Sobiesierski, A. J. Seeds, I. Ross, P. M. Smowton, and H. Liu, “Electrically pumped continuous-wave III–V quantum dot lasers on silicon,” Nat. Photonics 10, 307–311 (2016).
[Crossref]

B. Jang, K. Tanabe, S. Kako, S. Iwamoto, T. Tsuchizawa, H. Nishi, N. Hatori, M. Noguchi, T. Nakamura, K. Takemasa, M. Sugawara, and Y. Arakawa, “A hybrid silicon evanescent quantum dot laser,” Appl. Phys. Express 9, 092102 (2016).
[Crossref]

D. Liang, X. Huang, G. Kurczveil, M. Fiorentino, and R. G. Beausoleil, “Integrated finely tunable microring laser on silicon,” Nat. Photonics 10, 719–722 (2016).
[Crossref]

2015 (3)

C. Zhang, D. Liang, G. Kurczveil, J. E. Bowers, and R. G. Beausoleil, “Thermal management of hybrid silicon ring lasers for high temperature operation,” IEEE J. Sel. Top. Quantum Electron. 21, 1–7 (2015).
[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, 534 (2015).
[Crossref]

A. Arbabi, S. M. Kamali, E. Arbabi, B. G. Griffin, and L. L. Goddard, “Grating integrated single mode microring laser,” Opt. Express 23, 5335–5347 (2015).
[Crossref]

2014 (2)

G. H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar, G. Levaufre, N. Girard, F. Lelarge, J. M. Fedeli, A. Descos, B. Ben Bakir, S. Messaoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D. J. Thomson, F. Y. Gardes, and G. T. Reed, “Hybrid III–V on silicon lasers for photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 20, 158–170 (2014).
[Crossref]

A. Y. Liu, C. Zhang, J. Norman, A. Snyder, D. Lubyshev, J. M. Fastenau, A. W. K. Liu, A. C. Gossard, and J. E. Bowers, “High performance continuous wave 1.3  μm quantum dot lasers on silicon,” Appl. Phys. Lett. 104, 041104 (2014).
[Crossref]

2013 (1)

M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, T. Yongbo, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” J. Sel. Top. Quantum Electron. 19, 6100117 (2013).
[Crossref]

2012 (1)

A. E. Zhukov, M. V. Maksimov, and A. R. Kovsh, “Device characteristics of long-wavelength lasers based on self-organized quantum dots,” Semiconductors 46, 1225–1250 (2012).
[Crossref]

2010 (2)

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

2009 (2)

2008 (2)

J. Van Campenhout, L. Liu, P. R. Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. M. Fedeli, and R. Baets, “A compact SOI-integrated multiwavelength laser source based on cascaded InP microdisks,” IEEE Photon. Technol. Lett. 20, 1345–1347 (2008).
[Crossref]

Z. Mi and P. Bhattacharya, “Pseudomorphic and metamorphic quantum dot heterostructures for long-wavelength lasers on GaAs and Si,” IEEE J. Sel. Top. Quantum Electron. 14, 1171–1179 (2008).
[Crossref]

2007 (2)

2006 (4)

G. Roelkens, D. Van Thourhout, R. Baets, R. Notzel, and M. Smit, “Laser emission and photodetection in an InP/InGaAsP layer integrated on and coupled to a silicon-on-insulator waveguide circuit,” Opt. Express 14, 8154–8159 (2006).
[Crossref]

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14, 9203–9210 (2006).
[Crossref]

G. Ortner, C. N. Allen, C. Dion, P. Barrios, D. Poitras, D. Dalacu, G. Pakulski, J. Lapointe, P. J. Poole, W. Render, and S. Raymond, “External cavity InAs/InP quantum dot laser with a tuning range of 166  nm,” Appl. Phys. Lett. 88, 121119 (2006).
[Crossref]

S. A. Moore, L. O. Faolain, M. A. Cataluna, M. B. Flynn, M. V. Kotlyar, and T. F. Krauss, “Reduced surface sidewall recombination and diffusion in quantum-dot lasers,” Photon. Technol. Lett. 18, 1861–1863(2006).
[Crossref]

2005 (1)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

2000 (1)

G. Park, O. B. Shchekin, D. L. Huffaker, and D. G. Deppe, “Low-threshold oxide-confined 1.3  μm quantum-dot laser,” Photon. Technol. Lett. 12, 230–232 (2000).
[Crossref]

Accard, A.

G. H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar, G. Levaufre, N. Girard, F. Lelarge, J. M. Fedeli, A. Descos, B. Ben Bakir, S. Messaoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D. J. Thomson, F. Y. Gardes, and G. T. Reed, “Hybrid III–V on silicon lasers for photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 20, 158–170 (2014).
[Crossref]

Adelmini, L.

L. Sanchez, F. Fournel, B. Montmayeul, L. Bally, B. Szelag, and L. Adelmini, “Collective die direct bonding for photonic on silicon,” Electrochem. Soc. Trans. 86, 223–231 (2018).
[Crossref]

Aihara, T.

T. Hiraki, T. Aihara, K. Hasebe, K. Takeda, T. Fujii, T. Kakitsuka, T. Tsuchizawa, H. Fukuda, and S. Matsuo, “Heterogeneously integrated III–V/Si MOS capacitor Mach–Zehnder modulator,” Nat. Photonics 11, 482–485 (2017).
[Crossref]

Allen, C. N.

G. Ortner, C. N. Allen, C. Dion, P. Barrios, D. Poitras, D. Dalacu, G. Pakulski, J. Lapointe, P. J. Poole, W. Render, and S. Raymond, “External cavity InAs/InP quantum dot laser with a tuning range of 166  nm,” Appl. Phys. Lett. 88, 121119 (2006).
[Crossref]

Alloatti, L.

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G. Kurczveil, A. Seyedi, D. Liang, M. Fiorentino, and R. G. Beausoleil, “Error-free operation in a hybrid-silicon quantum dot comb laser,” Photon. Technol. Lett. 30, 71–74 (2018).
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C. Zhang, D. Liang, G. Kurczveil, J. E. Bowers, and R. G. Beausoleil, “Thermal management of hybrid silicon ring lasers for high temperature operation,” IEEE J. Sel. Top. Quantum Electron. 21, 1–7 (2015).
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D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. Spencer, Y.-H. Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, and J. E. Bowers, “Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,” Opt. Express 17, 20355–20364 (2009).
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G. H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar, G. Levaufre, N. Girard, F. Lelarge, J. M. Fedeli, A. Descos, B. Ben Bakir, S. Messaoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D. J. Thomson, F. Y. Gardes, and G. T. Reed, “Hybrid III–V on silicon lasers for photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 20, 158–170 (2014).
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Bowers, J. E.

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D. Dai, D. Liang, and J. E. Bowers, “Enhancement of the evanescent coupling between deeply-etched IIIV-Si hybrid microring laser and its small Si bus waveguide by using a bending coupler,” in Asia Communications and Photonics Conference and Exhibition, Shanghai, China (2009).

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S. A. Moore, L. O. Faolain, M. A. Cataluna, M. B. Flynn, M. V. Kotlyar, and T. F. Krauss, “Reduced surface sidewall recombination and diffusion in quantum-dot lasers,” Photon. Technol. Lett. 18, 1861–1863(2006).
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Chen, S.

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M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
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Di Cioccio, L.

J. Van Campenhout, L. Liu, P. R. Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. M. Fedeli, and R. Baets, “A compact SOI-integrated multiwavelength laser source based on cascaded InP microdisks,” IEEE Photon. Technol. Lett. 20, 1345–1347 (2008).
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Dion, C.

G. Ortner, C. N. Allen, C. Dion, P. Barrios, D. Poitras, D. Dalacu, G. Pakulski, J. Lapointe, P. J. Poole, W. Render, and S. Raymond, “External cavity InAs/InP quantum dot laser with a tuning range of 166  nm,” Appl. Phys. Lett. 88, 121119 (2006).
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Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
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M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, T. Yongbo, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” J. Sel. Top. Quantum Electron. 19, 6100117 (2013).
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G. H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar, G. Levaufre, N. Girard, F. Lelarge, J. M. Fedeli, A. Descos, B. Ben Bakir, S. Messaoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D. J. Thomson, F. Y. Gardes, and G. T. Reed, “Hybrid III–V on silicon lasers for photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 20, 158–170 (2014).
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Elliott, S. N.

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Fang, A. W.

Fang, K.

Faolain, L. O.

S. A. Moore, L. O. Faolain, M. A. Cataluna, M. B. Flynn, M. V. Kotlyar, and T. F. Krauss, “Reduced surface sidewall recombination and diffusion in quantum-dot lasers,” Photon. Technol. Lett. 18, 1861–1863(2006).
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A. Y. Liu, C. Zhang, J. Norman, A. Snyder, D. Lubyshev, J. M. Fastenau, A. W. K. Liu, A. C. Gossard, and J. E. Bowers, “High performance continuous wave 1.3  μm quantum dot lasers on silicon,” Appl. Phys. Lett. 104, 041104 (2014).
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Fedeli, J. M.

G. H. Duan, C. Jany, A. Le Liepvre, A. Accard, M. Lamponi, D. Make, P. Kaspar, G. Levaufre, N. Girard, F. Lelarge, J. M. Fedeli, A. Descos, B. Ben Bakir, S. Messaoudene, D. Bordel, S. Menezo, G. de Valicourt, S. Keyvaninia, G. Roelkens, D. Van Thourhout, D. J. Thomson, F. Y. Gardes, and G. T. Reed, “Hybrid III–V on silicon lasers for photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 20, 158–170 (2014).
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Feng, K.

D. Jung, R. Herrick, J. Norman, K. Turnlund, C. Jan, K. Feng, A. C. Gossard, and J. E. Bowers, “Impact of threading dislocation density on the lifetime of InAs quantum dot lasers on Si,” Appl. Phys. Lett. 112, 153507 (2018).
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G. Kurczveil, A. Seyedi, D. Liang, M. Fiorentino, and R. G. Beausoleil, “Error-free operation in a hybrid-silicon quantum dot comb laser,” Photon. Technol. Lett. 30, 71–74 (2018).
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D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. Spencer, Y.-H. Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, and J. E. Bowers, “Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,” Opt. Express 17, 20355–20364 (2009).
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D. Liang, C. Zhang, A. Roshan-Zamir, K. Yu, C. Li, G. Kurczveil, Y. Hu, W. Shen, M. Fiorentino, S. Kumar, S. Palermo, and R. Beausoleil, “A fully-integrated multi-λ hybrid DML transmitter,” presented at the Optical Fiber Communication Conference, San Diego, CA, USA (2018).

Flynn, M. B.

S. A. Moore, L. O. Faolain, M. A. Cataluna, M. B. Flynn, M. V. Kotlyar, and T. F. Krauss, “Reduced surface sidewall recombination and diffusion in quantum-dot lasers,” Photon. Technol. Lett. 18, 1861–1863(2006).
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Rojo Romeo, P.

Romeo, P. R.

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D. Liang, C. Zhang, A. Roshan-Zamir, K. Yu, C. Li, G. Kurczveil, Y. Hu, W. Shen, M. Fiorentino, S. Kumar, S. Palermo, and R. Beausoleil, “A fully-integrated multi-λ hybrid DML transmitter,” presented at the Optical Fiber Communication Conference, San Diego, CA, USA (2018).

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S. Chen, W. Li, J. Wu, Q. Jiang, M. Tang, S. Shutts, S. N. Elliott, A. Sobiesierski, A. J. Seeds, I. Ross, P. M. Smowton, and H. Liu, “Electrically pumped continuous-wave III–V quantum dot lasers on silicon,” Nat. Photonics 10, 307–311 (2016).
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Seassal, C.

J. Van Campenhout, L. Liu, P. R. Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. M. Fedeli, and R. Baets, “A compact SOI-integrated multiwavelength laser source based on cascaded InP microdisks,” IEEE Photon. Technol. Lett. 20, 1345–1347 (2008).
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G. Park, O. B. Shchekin, D. L. Huffaker, and D. G. Deppe, “Low-threshold oxide-confined 1.3  μm quantum-dot laser,” Photon. Technol. Lett. 12, 230–232 (2000).
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D. Liang, C. Zhang, A. Roshan-Zamir, K. Yu, C. Li, G. Kurczveil, Y. Hu, W. Shen, M. Fiorentino, S. Kumar, S. Palermo, and R. Beausoleil, “A fully-integrated multi-λ hybrid DML transmitter,” presented at the Optical Fiber Communication Conference, San Diego, CA, USA (2018).

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D. Huang, P. Pintus, C. Zhang, Y. Shoji, T. Mizumoto, and J. E. Bowers, “Electrically driven and thermally tunable integrated optical isolators for silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 22, 271–278 (2016).
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Smit, M.

Smit, M. K.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
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Figures (5)

Fig. 1.
Fig. 1. Schematic structure of the hybrid QD microring laser on silicon and its fabrication process: (a) passive components fabrication on SOI, (b) GaAs substrate bonding to transfer QD gain layers to SOI, (c) p-metal deposition and ring mesa formation, (d) n-metal deposition and residual III–V removal, (e) passivation and probe metal deposition, (f) schematic cross-section of the microring mesa, and (g) its SEM image.
Fig. 2.
Fig. 2. (a) Simulated coupling efficiency at different offsets as a function of angle θ of the curved coupling section for fundamental TE mode injection in the ring and corresponding top-view electrical field profiles for (b) θ=75 and (c) θ=105 under zero offset. Light injection location is highlighted by the yellow arrow in (b).
Fig. 3.
Fig. 3. (a) Temperature distribution at the cross-section of the hybrid QD microring laser with 50 μm diameter, 5 μm mesa width, and 1 μm BOX under 100 mW dissipation power; (b) simulated thermal impedance of hybrid QD microring laser with 50 μm diameter and varying mesa width and BOX thickness.
Fig. 4.
Fig. 4. (a) LIV curve of a typical hybrid QD microring laser at 20°C, (b) temperature-dependent LI curves, and (c) the function of threshold current and maximum output power with different stage temperatures, (d) the output lasing spectrum at 20°C and 50°C, respectively, (e) the summary of threshold current, and (f) maximum output power distributions of 50 μm diameter hybrid QD ring lasers with varied coupling gaps, coupling angles, and WG offsets.
Fig. 5.
Fig. 5. (a) Small signal response of the hybrid QD microring laser under varied bias current, (b) schematic of the laser modulation experiment, (c) NRZ eye diagrams at 12.5 Gb/s and 15 Gb/s data rate, and (d) corresponding bathtub plot with data error rate.