Abstract

Quantum-dash (QD) mode-locked laser diodes (MLLD) lend themselves as chip-scale frequency comb generators for highly scalable wavelength-division multiplexing (WDM) links in future data-center, campus-area, or metropolitan networks. Driven by a simple DC current, the devices generate flat broadband frequency combs, containing tens of equidistant optical tones with line spacings of tens of GHz. Here we show that QD-MLLDs can not only be used as multi-wavelength light sources at a WDM transmitter, but also as multi-wavelength local oscillators (LO) for parallel coherent reception. In our experiments, we demonstrate transmission of an aggregate net data rate of 3.9 Tbit/s (23 × 45 GBd PDM-QPSK, 7% FEC overhead) over 75 km standard single-mode fiber (SSMF). To the best of our knowledge, this represents the first demonstration of a coherent WDM link that relies on QD-MLLD both at the transmitter and the receiver.

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

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2018 (8)

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

A. Fülöp, M. Mazur, A. Lorences-Riesgo, O. B. Helgason, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators,” Nat. Commun. 9(1), 1598 (2018).
[Crossref] [PubMed]

C. Doerr and L. Chen, “Silicon photonics in optical coherent systems,” Proc. IEEE 106(12), 2291–2301 (2018).
[Crossref]

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

S. L. I. Olsson, J. Cho, S. Chandrasekhar, X. Chen, P. J. Winzer, and S. Makovejs, “Probabilistically shaped PDM 4096-QAM transmission over up to 200 km of fiber using standard intradyne detection,” Opt. Express 26(4), 4522–4530 (2018).
[Crossref] [PubMed]

M. Mazur, A. Lorences-Riesgo, J. Schroder, P. A. Andrekson, and M. Karlsson, “High spectral efficiency PM-128QAM comb-based superchannel transmission enabled by a single shared optical pilot tone,” J. Lightwave Technol. 36(6), 1318–1325 (2018).
[Crossref]

Z. G. Lu, J. R. Liu, P. J. Poole, C. Y. Song, and S. D. Chang, “Ultra-narrow linewidth quantum dot coherent comb lasers with self-injection feedback locking,” Opt. Express 26(9), 11909–11914 (2018).
[Crossref] [PubMed]

2017 (1)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (2)

2014 (3)

C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014).
[Crossref] [PubMed]

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (7)

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
[Crossref]

K. Kikuchi, “Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers,” Opt. Express 20(5), 5291–5302 (2012).
[Crossref] [PubMed]

R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
[Crossref] [PubMed]

R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

2011 (4)

M. T. Crowley, D. Murrell, N. Patel, M. Breivik, C.-Y. Lin, Y. Li, B.-O. Fimland, and L. F. Lester, “Analytical modeling of the temperature performance of monolithic passively mode-locked quantum dot lasers,” IEEE J. Quantum Electron. 47(8), 1059–1068 (2011).
[Crossref]

P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
[Crossref]

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
[Crossref]

T. Flick, K. H. Becks, J. Dopke, P. Mättig, and P. Tepel, “Measurement of the thermal resistance of VCSEL devices,” J. Instrum. 6, C01021 (2011).
[Crossref]

2010 (1)

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (1)

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

2006 (1)

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
[Crossref]

2003 (1)

A. E. Zhukov, A. R. Kovsh, D. A. Livshits, V. M. Ustinov, and Z. I. Alferov, “Output power and its limitation in ridge-waveguide 1.3 m wavelength quantum-dot lasers,” Semicond. Sci. Technol. 18(8), 774–781 (2003).
[Crossref]

1978 (1)

D. N. Godard, “Passband timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
[Crossref]

Accard, A.

K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
[Crossref]

R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
[Crossref] [PubMed]

R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
[Crossref] [PubMed]

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
[Crossref]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
[Crossref]

Akrout, A.

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
[Crossref]

Alferov, Z. I.

A. E. Zhukov, A. R. Kovsh, D. A. Livshits, V. M. Ustinov, and Z. I. Alferov, “Output power and its limitation in ridge-waveguide 1.3 m wavelength quantum-dot lasers,” Semicond. Sci. Technol. 18(8), 774–781 (2003).
[Crossref]

Alic, N.

Alloatti, L.

Altenhain, L.

Ambrosius, H.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Amma, Y.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Anagnosti, M.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Anandarajah, P. M.

P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
[Crossref]

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

Andrekson, P. A.

A. Fülöp, M. Mazur, A. Lorences-Riesgo, O. B. Helgason, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators,” Nat. Commun. 9(1), 1598 (2018).
[Crossref] [PubMed]

M. Mazur, A. Lorences-Riesgo, J. Schroder, P. A. Andrekson, and M. Karlsson, “High spectral efficiency PM-128QAM comb-based superchannel transmission enabled by a single shared optical pilot tone,” J. Lightwave Technol. 36(6), 1318–1325 (2018).
[Crossref]

Ataie, V.

Aubin, G.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
[Crossref]

Augustin, L. M.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Azouigui, S.

K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
[Crossref]

Bakker, A.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Barletta, L.

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
[Crossref]

Barry, L.

P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
[Crossref]

Barry, L. P.

Becker, J.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Becks, K. H.

T. Flick, K. H. Becks, J. Dopke, P. Mättig, and P. Tepel, “Measurement of the thermal resistance of VCSEL devices,” J. Instrum. 6, C01021 (2011).
[Crossref]

Behnia, B.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Bekele, D.

Ben-Ezra, S.

Bertolini, M.

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
[Crossref]

Bogaerts, W.

Bolk, J.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Breivik, M.

M. T. Crowley, D. Murrell, N. Patel, M. Breivik, C.-Y. Lin, Y. Li, B.-O. Fimland, and L. F. Lester, “Analytical modeling of the temperature performance of monolithic passively mode-locked quantum dot lasers,” IEEE J. Quantum Electron. 47(8), 1059–1068 (2011).
[Crossref]

Brenot, R.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
[Crossref]

Buggaveeti, S.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Butrie, T.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Calo, C.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

Chandrasekhar, S.

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Chang, S. D.

Chen, L.

C. Doerr and L. Chen, “Silicon photonics in optical coherent systems,” Proc. IEEE 106(12), 2291–2301 (2018).
[Crossref]

Chen, X.

Chimot, N.

F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
[Crossref]

Cho, J.

Corzine, S. W.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Croussore, K.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Crowley, M. T.

M. T. Crowley, D. Murrell, N. Patel, M. Breivik, C.-Y. Lin, Y. Li, B.-O. Fimland, and L. F. Lester, “Analytical modeling of the temperature performance of monolithic passively mode-locked quantum dot lasers,” IEEE J. Quantum Electron. 47(8), 1059–1068 (2011).
[Crossref]

Da Ros, F.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Dagens, B.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Dalton, L. R.

den Haan, E.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Derouin, E.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Dijk, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Doerr, C.

C. Doerr and L. Chen, “Silicon photonics in optical coherent systems,” Proc. IEEE 106(12), 2291–2301 (2018).
[Crossref]

Dopke, J.

T. Flick, K. H. Becks, J. Dopke, P. Mättig, and P. Tepel, “Measurement of the thermal resistance of VCSEL devices,” J. Instrum. 6, C01021 (2011).
[Crossref]

Dreschmann, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

Drisse, O.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Duan, G.-H.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Elder, D.

Ellermeyer, T.

Evans, P.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Farrow, C. W.

C. W. Farrow, “A continuously variable digital delay element,” in IEEE International Symposium on Circuits and Systems (IEEE, 1988), pp. 2641–2645.

Fimland, B.-O.

M. T. Crowley, D. Murrell, N. Patel, M. Breivik, C.-Y. Lin, Y. Li, B.-O. Fimland, and L. F. Lester, “Analytical modeling of the temperature performance of monolithic passively mode-locked quantum dot lasers,” IEEE J. Quantum Electron. 47(8), 1059–1068 (2011).
[Crossref]

Flick, T.

T. Flick, K. H. Becks, J. Dopke, P. Mättig, and P. Tepel, “Measurement of the thermal resistance of VCSEL devices,” J. Instrum. 6, C01021 (2011).
[Crossref]

Freude, W.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

J. N. Kemal, J. Pfeifle, P. Marin-Palomo, M. D. G. Pascual, S. Wolf, F. Smyth, W. Freude, and C. Koos, “Multi-wavelength coherent transmission using an optical frequency comb as a local oscillator,” Opt. Express 24(22), 25432–25445 (2016).
[Crossref] [PubMed]

J. Pfeifle, V. Vujicic, R. T. Watts, P. C. Schindler, C. Weimann, R. Zhou, W. Freude, L. P. Barry, and C. Koos, “Flexible terabit/s Nyquist-WDM super-channels using a gain-switched comb source,” Opt. Express 23(2), 724–738 (2015).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Fülöp, A.

A. Fülöp, M. Mazur, A. Lorences-Riesgo, O. B. Helgason, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators,” Nat. Commun. 9(1), 1598 (2018).
[Crossref] [PubMed]

Galili, M.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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Gavioli, G.

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
[Crossref]

Geyer, J.

T. Pfau, H. Zhang, J. Geyer, and C. Rasmussen, “High performance coherent ASIC,” in European Conference on Optical Communication (ECOC, 2018), pp. 1–3.

Godard, D. N.

D. N. Godard, “Passband timing recovery in an all-digital modem receiver,” IEEE Trans. Commun. 26(5), 517–523 (1978).
[Crossref]

Going, R. W.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Gosset, C.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
[Crossref]

Gouezigou, O. L.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

Guan, P.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Hartinger, K.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Helgason, O. B.

A. Fülöp, M. Mazur, A. Lorences-Riesgo, O. B. Helgason, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators,” Nat. Commun. 9(1), 1598 (2018).
[Crossref] [PubMed]

Herr, T.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Hillerkuss, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

Hoffmann, S.

Holzwarth, R.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Hosseini, A.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Hu, H.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Huebner, M.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Huynh, T. N.

Ingerslev, K.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Jordan, M.

Josten, A.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Karanicolas, A.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Karlsson, M.

Karpov, M.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

Kemal, J. N.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

J. N. Kemal, J. Pfeifle, P. Marin-Palomo, M. D. G. Pascual, S. Wolf, F. Smyth, W. Freude, and C. Koos, “Multi-wavelength coherent transmission using an optical frequency comb as a local oscillator,” Opt. Express 24(22), 25432–25445 (2016).
[Crossref] [PubMed]

Kikuchi, K.

Kim, N.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Kippenberg, T. J.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Kish, F.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Kleijn, S.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Kleinow, P.

Koeber, S.

Koenig, S.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Koos, C.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

J. N. Kemal, J. Pfeifle, P. Marin-Palomo, M. D. G. Pascual, S. Wolf, F. Smyth, W. Freude, and C. Koos, “Multi-wavelength coherent transmission using an optical frequency comb as a local oscillator,” Opt. Express 24(22), 25432–25445 (2016).
[Crossref] [PubMed]

J. Pfeifle, V. Vujicic, R. T. Watts, P. C. Schindler, C. Weimann, R. Zhou, W. Freude, L. P. Barry, and C. Koos, “Flexible terabit/s Nyquist-WDM super-channels using a gain-switched comb source,” Opt. Express 23(2), 724–738 (2015).
[Crossref] [PubMed]

C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

Kordts, A.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

Korn, D.

Korthorst, T.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Kovsh, A. R.

A. E. Zhukov, A. R. Kovsh, D. A. Livshits, V. M. Ustinov, and Z. I. Alferov, “Output power and its limitation in ridge-waveguide 1.3 m wavelength quantum-dot lasers,” Semicond. Sci. Technol. 18(8), 774–781 (2003).
[Crossref]

Kuntz, M.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Kuo, B. P.-P.

Lafosse, X.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

Lal, V.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
[Crossref]

Landreau, J.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
[Crossref]

Latkowski, S.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

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K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
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K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
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R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
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R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
[Crossref] [PubMed]

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
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K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
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R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
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Merghem, K.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
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K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
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R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
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R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
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R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
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R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
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P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
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M. T. Crowley, D. Murrell, N. Patel, M. Breivik, C.-Y. Lin, Y. Li, B.-O. Fimland, and L. F. Lester, “Analytical modeling of the temperature performance of monolithic passively mode-locked quantum dot lasers,” IEEE J. Quantum Electron. 47(8), 1059–1068 (2011).
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D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
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H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
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P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
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R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
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H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
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M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
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Pfau, T.

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
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T. Pfau, H. Zhang, J. Geyer, and C. Rasmussen, “High performance coherent ASIC,” in European Conference on Optical Communication (ECOC, 2018), pp. 1–3.

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P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
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C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014).
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Phelan, R.

P. M. Anandarajah, R. Maher, Y. Xu, S. Latkowski, J. O’Carroll, S. G. Murdoch, R. Phelan, J. O’Gorman, and L. Barry, “Generation of coherent multicarrier signals by gain switching of discrete mode lasers,” IEEE Photonics J. 3(1), 112–122 (2011).
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F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
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F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
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F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
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F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
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Porto da Silva, E.

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F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
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H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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Rahn, J. T.

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Ramdane, A.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
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K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
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R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
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R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
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R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
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C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau, and F. Lelarge, “Subpicosecond pulse generation at 134GHz using a quantum-dash-based Fabry-Perot laser emitting at 1.56μm,” Appl. Phys. Lett. 88(24), 241105 (2006).
[Crossref]

Rasmussen, C.

T. Pfau, H. Zhang, J. Geyer, and C. Rasmussen, “High performance coherent ASIC,” in European Conference on Optical Communication (ECOC, 2018), pp. 1–3.

Renaudier, J.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
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Resan, B.

Richter, A.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
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Rosales, R.

K. Merghem, C. Calo, R. Rosales, X. Lafosse, G. Aubin, A. Martinez, F. Lelarge, and A. Ramdane, “Stability of optical frequency comb generated with InAs/InP quantum-dash-based passive mode-locked lasers,” IEEE J. Quantum Electron. 50(4), 275–280 (2014).
[Crossref]

K. Merghem, R. Rosales, S. Azouigui, Q. Zou, A. Martinez, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum dot based lasers and effect of optical feedback,” Proc. SPIE 8277, 82770D (2012).
[Crossref]

R. Rosales, K. Merghem, A. Martinez, F. Lelarge, A. Accard, and A. Ramdane, “Timing jitter from the optical spectrum in semiconductor passively mode locked lasers,” Opt. Express 20(8), 9151–9160 (2012).
[Crossref] [PubMed]

R. Rosales, S. G. Murdoch, R. T. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20(8), 8649–8657 (2012).
[Crossref] [PubMed]

R. Rosales, K. Merghem, A. Martinez, A. Akrout, J.-P. Tourrenc, A. Accard, F. Lelarge, and A. Ramdane, “InAs/InP quantum-dot passively mode-locked lasers for 1.55-μ m applications,” IEEE J. Sel. Top. Quantum Electron. 17, 1292–1301 (2011).
[Crossref]

Rosenberger, R.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546(7657), 274–279 (2017).
[Crossref] [PubMed]

Rousseau, B.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. Dijk, D. Make, O. L. Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007).
[Crossref]

F. Lelarge, R. Brenot, B. Rousseau, F. Martin, F. Poingt, L. LeGouezigou, O. Le Gouezigou, F. Pommereau, A. Accard, D. Make, N. Chimot, and F. Van-Dijk, “Effect of P-doping on temperature and dynamic performances of 1550nm InAs/InP Quantum Dash based lasers,” in IEEE International Conference on Indium Phosphide & Related Materials (IEEE, 2009), pp. 383–386.
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Santos, R.

L. M. Augustin, R. Santos, E. den Haan, S. Kleijn, P. J. A. Thijs, S. Latkowski, D. Zhao, W. Yao, J. Bolk, H. Ambrosius, S. Mingaleev, A. Richter, A. Bakker, and T. Korthorst, “InP-based generic foundry platform for photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24(1), 1–10 (2018).
[Crossref]

Sasaki, Y.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
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Savory, S. J.

Schindler, P.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Schindler, P. C.

Schmogrow, R.

C. Weimann, P. C. Schindler, R. Palmer, S. Wolf, D. Bekele, D. Korn, J. Pfeifle, S. Koeber, R. Schmogrow, L. Alloatti, D. Elder, H. Yu, W. Bogaerts, L. R. Dalton, W. Freude, J. Leuthold, and C. Koos, “Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission,” Opt. Express 22(3), 3629–3637 (2014).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. C. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single-laser 32.5 Tbit/s Nyquist WDM transmission,” J. Opt. Commun. Netw. 4(10), 715–723 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012). Erratum: ibid. 24(23), 2198 (2012).

Schroder, J.

Semenova, E.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Smyth, F.

Song, C. Y.

Spalvieri, A.

M. Magarini, L. Barletta, A. Spalvieri, F. Vacondio, T. Pfau, M. Pepe, M. Bertolini, and G. Gavioli, “Pilot-symbols-aided carrier-phase recovery for 100-G PM-QPSK digital coherent receivers,” IEEE Photonics Technol. Lett. 24(9), 739–741 (2012).
[Crossref]

Studenkov, P.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
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Summers, J.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
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Tang, J.

R. W. Going, M. Lauermann, R. Maher, H.-S. Tsai, A. Hosseini, M. Lu, N. Kim, P. Studenkov, S. W. Corzine, J. Summers, M. Anagnosti, M. Montazeri, J. Zhang, B. Behnia, J. Tang, S. Buggaveeti, T. Vallaitis, J. Osenbach, M. Kuntz, X. Xu, K. Croussore, V. Lal, P. Evans, J. T. Rahn, T. Butrie, A. Karanicolas, K.-T. Wu, M. Mitchell, M. Ziari, D. Welch, and F. Kish, “1.00 (0.88) Tb/s per wave capable coherent multi-channel transmitter (receiver) InP-based PICs with hybrid integrated SiGe electronics,” IEEE J. Quantum Electron. 54(4), 1–10 (2018).
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Temprana, E.

Tepel, P.

T. Flick, K. H. Becks, J. Dopke, P. Mättig, and P. Tepel, “Measurement of the thermal resistance of VCSEL devices,” J. Instrum. 6, C01021 (2011).
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Figures (6)

Fig. 1
Fig. 1 Setup of a coherent WDM transmission link using optical frequency combs as light sources both at the transmitter and the receiver. WDM transmitter: Carriers from a transmitter comb (Tx comb) are demultiplexed (DEMUX) and modulated separately using in-phase/quadrature modulators (IQ mod.). The channels are then multiplexed (MUX) to form the WDM signal. Link: The WDM signal is amplified and transmitted. WDM receiver: The channels are demultiplexed and sent to an array of independent coherent receivers (Coh. Rx). The demultiplexed spectral lines of a local oscillator comb (LO comb) serve as LO tones for the various coherent receivers. EDFA: Erbium-doped fiber amplifier.
Fig. 2
Fig. 2 Concept and characterization of quantum-dash mode-locked laser diodes (QD-MLLD). (a) Three-dimensional schematic of a QD-MLLD. The active region consists of three stacked layers of InAs QD, which are separated by InGaAsP barriers. The buried ridge waveguide has a width of 1.0 µm. Cleaved chip facets form a Fabry-Perot laser cavity with a length of 1.71 mm, leading to an FSR of 25 GHz. Top and bottom gold layers provide electrical contacts to the active region of the QD-MLLD via p-doped and n-doped InP layers. (b) Basic optical setup for using the QD-MLLD comb source. The device is driven by a constant injection current (not shown). The emitted light is collected by a lensed fiber, and an optical isolator is used to reduce back-reflections into the QD-MLLD. Setups C, D, and E are used for measuring the data of Subfigures (c), (d), and (e), respectively. PM: Power meter; ESA: Electrical spectrum analyzer; OSA: Optical spectrum analyzer. (c) Measured total comb power versus injection current of the Tx and the LO combs. (d) Full-width half maximum (FWHM) of the radio-frequency (RF) beat note (upper plot) as a function of the drive current for the Tx comb (blue) and for the LO comb (red), and free spectral range (FSR, lower plot) as a function of the drive current for the Tx comb (blue), and for the LO comb (red). For some drive currents, we observe distinctively higher RF linewidths, see, e.g., Point I. In these cases, we often observe more than one beat note in the RF spectrum, Inset I, which we attribute to the coexistence of two sub-combs with slightly different FSR [33]. For such operating states, the depicted large RF linewidth values are to be understood as an indication of unstable operation by the MLLD. Inset II shows the measured RF beat note corresponding to a stable single sub-comb operation of the QD-MLLD. In the insets, the spectral power is normalized to the dominant peak, and the frequency axis is defined with respect to the spectral position of this peak. (e) Optical power spectra of the Tx comb (blue) and the LO comb (red). RBW: Resolution bandwidth of the OSA.
Fig. 3
Fig. 3 Phase-noise characterization of QD-MLLD. (a) Experimental setup. Narrow-band tunable band-pass filters (TBF) are used to select distinct lines with comparable frequencies from the Tx comb and the LO comb. A polarization controller (PC) is used to match the polarizations of the selected tones at the input of a 90° optical hybrid. Balanced photodetectors (BPD) deliver the electrical in-phase (I) and quadrature (Q) signals, which are sampled with a real-time oscilloscope (RTO) for offline processing. (b) Power spectrum of the beat note between the two tones selected from the Tx comb and the LO comb as a function of the offset from the beat note frequency (green trace). The duration of the corresponding time-domain signals is 0.4 µs. We use the IQ data to independently extract a short-term Lorentzian linewidth of 5.1 MHz. The associated line shape (red trace) coincides well with the measured spectrum
Fig. 4
Fig. 4 Coherent WDM transmission experiment using QD-MLLD comb generators both as a multi-wavelength light source at the transmitter (Tx) and as a multi-wavelength LO at the receiver (Rx). (a) Experimental setup: The Tx comb is de-interleaved into even and odd carriers using a programmable filter (PF-1). The two sets of carriers are then modulated with independent data streams to emulate a real WDM signal with independent data on neighboring channels. Polarization-division multiplexing (PDM) is emulated by splitting the single-polarization WDM signal into two paths, delaying one of them, and recombining the two decorrelated signals on orthogonal polarizations of the transmission fiber. At the receiver, we subsequently select individual lines of an LO comb and use them for coherent detection of the corresponding WDM channel. The WDM channels are spaced by approximately 50 GHz and carry QPSK signals at symbol rates of 45 GBd, limited by the bandwidth of the arbitrary-waveform generator (AWG) used to generate the modulator drive signals at the Tx. P1, P2, and P3 denote points in the experimental setup at which the optical spectra in Subfigure (b) have been taken. EDFA: Erbium-doped fiber amplifier, IQ: In-phase/quadrature modulator; DL: Delay line; VOA: Variable optical attenuator; PBC: Polarization beam combiner; TBF: Tunable band-pass filter; SSMF: Standard single-mode fiber; ESA: Electrical spectrum analyzer; CD: Chromatic dispersion; MIMO: Multiple-input and multiple-output. (b) Comb spectra of both even and odd carriers before modulation (upper plot, P1), spectrum of 23 modulated carriers (lower plot, P2), and spectrum of the LO comb (lower plot, P3). (c) RF beat note of each comb obtained by impinging the output of the two QD-MLLDs on a photodetector simultaneously as depicted in Subfigure (a).
Fig. 5
Fig. 5 Coherent data transmission performance obtained by using a QD-MLLD comb generator both as the Tx light source and as the LO. (a) Upper plot: Measured EVM as a function of the carrier frequency of the transmitted channels for both back-to-back (btb, ▲) and 75 km SSMF transmission (■). Lower plot: BER estimated from EVM assuming that the QPSK signals are impaired by additive white Gaussian noise only [46]. (b) Example constellation diagrams for the signal carried by the comb line at 194.15 THz, both for back-to-back (btb) and for 75 km fiber transmission.
Fig. 6
Fig. 6 Comparison of transmission performance obtained by using a QD-MLLD and a conventional external-cavity lasers (ECL) as LO tone generators. (a) Experimental setup. At the Tx, we use an ECL having a linewidth below 100 kHz as light source. The ECL carrier is boosted by an EDFA (EDFA-1) and modulated with a QPSK signal at a symbol rate of 45 GBd. The length of the underlying pseudo-random bit sequence amounts to 215 1. Polarization-division multiplexing (PDM) is emulated by the same method discussed in Section 3.1. The PDM signals are amplified by an EDFA (EDFA-2), filtered by a tunable bandpass filter (TBF), and sent to the signal input of a dual-polarization coherent receiver. The signal is detected by using either a QD-MLLD comb tone as an LO, or by using a second ECL. The LO is amplified by EDFA-3 and filtered by a programmable filter. A variable optical attenuator (VOA) in front of EDFA-4 is used to vary the optical carrier-to-noise power ratio (OCNR) of the LO tone. (b) BER vs. OCNR of the LO tone. The OCNR is indicated with respect to a reference noise bandwidth of 12.5 GHz (0.1 nm). We find that LO tones from a QD-MLLD (solid lines) perform similarly to an ECL LO (dotted lines).

Equations (1)

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Δf= lim τ0 σ Δϕ 2 (τ) 2πτ .

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