Abstract

We studied theoretically coherent phenomena in the multimode dynamics of single section semiconductor ring lasers with quantum dots (QDs) active region. In the unidirectional ring configuration our simulations show the occurrence of self-mode-locking in the system leading to ultra-short pulses (sub-picoseconds) with a terahertz repetition rate. As confirmed by the linear stability analysis (LSA) of the traveling wave (TW) solutions this phenomenon is triggered by an analogous of the Risken-Nummedal-Graham-Haken (RNGH) instability affecting the multimode dynamics of two-level lasers.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (1)

L. L. Columbo, P. Bardella, M. Gioannini, and Politecnico di Torino (Italy), “Spontaneous generation of frequency combs in QD lasers,” Proc. SPIEE 10553, 105530 (2018).

2017 (4)

2016 (2)

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

N. Vukovic, J. Radovanovic, V. Milanovic, and D. L. Boiko, “Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers,” Opt. Express 24, 26911–26929 (2016).
[Crossref] [PubMed]

2015 (2)

C.-H. Chen, M. A. Seyedi, M. Fiorentino, D. Livshits, A. Gubenko, S. Mikhrin, V. Mikhrin, and R. G. Beausoleil, “A comb laser-driven DWDM silicon photonic transmitter based on microring modulators,” Opt. Express 23, 21541–21548 (2015).
[Crossref] [PubMed]

M. Gioannini, P. Bardella, and I. Montrosset, “Time-domain traveling-wave analysis of the multimode dynamics of quantum dot Fabry-Perot lasers,” IEEE J. Sel. Top. Quantum Electron. 21, 698–708 (2015).
[Crossref]

2014 (1)

A. C. O. Karni, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Coherent control in a semiconductor optical amplifier operating at room temperature,” Nat. Commun. 5, 5025 (2014).
[Crossref] [PubMed]

2013 (2)

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

2011 (3)

M. Rossetti, P. Bardella, and I. Montrosset, “Time-domain travelling-wave model for quantum dot passively mode-locked lasers,” IEEE J. Quantum Electron. 47, 139–150 (2011).
[Crossref]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Perot lasers: the effect of spatial hole burning”, Opt. Express 19, 3284–3289 (2011).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

2010 (6)

H. Choi, V.-M. Gkortsas, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, F. Capasso, F. X. Kärtner, and T. B. Norris, “Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser,” Nat. Photonics 4, 706–711 (2010).
[Crossref]

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

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]

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers”, Phys. Rev. A,  81, 043817 (2010).
[Crossref]

L. Columbo and L. Gil, “Bistable self-starting pulses with terahertz repetition rate in a semiconductor microring laser”, Opt. Lett. 35, 1473–1475 (2010).
[Crossref]

2009 (1)

2008 (3)

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

J. Liu, Z. Lu, S. Raymond, P. J. Poole, P. J. Barrios, and D. Poitras, “Dual-wavelength 92.5 GHz self-mode-locked InP-based quantum dot laser,” Opt. Lett. 33, 1702–1704 (2008).
[Crossref] [PubMed]

S. Latkowski, F. Surre, and P. Landais, “Terahertz wave generation from a DC-biased multimode laser,” App. Phys. Lett. 92, 081109 (2008).
[Crossref]

2007 (1)

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

2006 (3)

T. W. Hänsch, “Nobel lecture: Passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

P. J. Delfyett, S. Gee, M.-T. Choi, H. Izadpanah, W. Lee, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol. 24, 2701–2719 (2006).
[Crossref]

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

2001 (2)

K. Sato, “100 GHz optical pulse generation using Fabry-Perot laser under continuous wave operation,” Electron. Lett. 37, 763–764 (2001).
[Crossref]

E. Roldan, G. J. de Valcarcel, F. Silva, and F. Prati, “Multimode emission in inhomogeneously broadened ring lasers,” J. Opt. Soc. Am. B 18, 1601–1611 (2001).
[Crossref]

1968 (1)

H. Risken and K. Nummedal, “Self pulsating in lasers,” J. App. Phys. 39, 4662–4672 (1968).
[Crossref]

Accard, A.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Akalin, T.

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

Ambacher, O.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Anantathanasarn, S.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Antes, J.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Aramideh, S.

N. Eiselt, H. Griesser, M. H. Eiselt, W. Kaiser, S. Aramideh, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Real-time 200 Gb/s (4×56.25 Gb/s) PAM-4 transmission over 80 km SSMF using quantum-dot laser and silicon ring-modulator,” in “Optical Fiber Communication Conference,” (2017), p. W4D.3.

Aubin, G.

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

Baets, R.

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]

Balle, S.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Perot lasers: the effect of spatial hole burning”, Opt. Express 19, 3284–3289 (2011).
[Crossref]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers”, Phys. Rev. A,  81, 043817 (2010).
[Crossref]

Barbarin, Y.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Bardella, P.

L. L. Columbo, P. Bardella, M. Gioannini, and Politecnico di Torino (Italy), “Spontaneous generation of frequency combs in QD lasers,” Proc. SPIEE 10553, 105530 (2018).

P. Bardella, L. L. Columbo, and M. Gioannini, “Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study,” Opt. Express 25, 26234–26252 (2017).
[Crossref] [PubMed]

M. Gioannini, P. Bardella, and I. Montrosset, “Time-domain traveling-wave analysis of the multimode dynamics of quantum dot Fabry-Perot lasers,” IEEE J. Sel. Top. Quantum Electron. 21, 698–708 (2015).
[Crossref]

M. Rossetti, P. Bardella, and I. Montrosset, “Time-domain travelling-wave model for quantum dot passively mode-locked lasers,” IEEE J. Quantum Electron. 47, 139–150 (2011).
[Crossref]

Barrios, P.

Barrios, P. J.

Beausoleil, R. G.

Beck, A.

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

Beck, M.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Belyanin, A.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Bente, E.A.J.M.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Bimberg, D.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Boes, F.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Boiko, D. L.

Bonzon, C.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Bour, D.

H. Choi, V.-M. Gkortsas, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, F. Capasso, F. X. Kärtner, and T. B. Norris, “Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser,” Nat. Photonics 4, 706–711 (2010).
[Crossref]

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L. L. Columbo, P. Bardella, M. Gioannini, and Politecnico di Torino (Italy), “Spontaneous generation of frequency combs in QD lasers,” Proc. SPIEE 10553, 105530 (2018).

P. Bardella, L. L. Columbo, and M. Gioannini, “Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study,” Opt. Express 25, 26234–26252 (2017).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Li, Q.

Lingnau, B.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Link, S. M.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Liu, H. C.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Liu, J.

Liu, L.

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]

Livshits, D.

Longhi, S.

Lopez-Diaz, D.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Lu, Z.

Lüdge, K.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
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Lugiato, L.

L. Lugiato, F. Prati, and M. Brambilla, Nonlinear Optical Systems (Cambridge University, 2015).
[Crossref]

Maas, D. J. H. C.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

MacFarlane, I.

Maier, T.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Make, D.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Maldonado-Basilio, R.

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
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Martinez, A.

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

Merghem, K.

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

Mikhrin, V.

Milanovic, V.

Monroy, I. T.

N. Eiselt, H. Griesser, M. H. Eiselt, W. Kaiser, S. Aramideh, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Real-time 200 Gb/s (4×56.25 Gb/s) PAM-4 transmission over 80 km SSMF using quantum-dot laser and silicon ring-modulator,” in “Optical Fiber Communication Conference,” (2017), p. W4D.3.

Montrosset, I.

M. Gioannini, P. Bardella, and I. Montrosset, “Time-domain traveling-wave analysis of the multimode dynamics of quantum dot Fabry-Perot lasers,” IEEE J. Sel. Top. Quantum Electron. 21, 698–708 (2015).
[Crossref]

M. Rossetti, P. Bardella, and I. Montrosset, “Time-domain travelling-wave model for quantum dot passively mode-locked lasers,” IEEE J. Quantum Electron. 47, 139–150 (2011).
[Crossref]

Moreau, G.

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

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).
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Norman, J.

Norris, T. B.

H. Choi, V.-M. Gkortsas, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, F. Capasso, F. X. Kärtner, and T. B. Norris, “Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser,” Nat. Photonics 4, 706–711 (2010).
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Nötzel, R.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Nshii, C. C.

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Nummedal, K.

H. Risken and K. Nummedal, “Self pulsating in lasers,” J. App. Phys. 39, 4662–4672 (1968).
[Crossref]

Oei, Y.S.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Olmos, J. J. V.

N. Eiselt, H. Griesser, M. H. Eiselt, W. Kaiser, S. Aramideh, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Real-time 200 Gb/s (4×56.25 Gb/s) PAM-4 transmission over 80 km SSMF using quantum-dot laser and silicon ring-modulator,” in “Optical Fiber Communication Conference,” (2017), p. W4D.3.

Owschimikow, N.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Ozharar, S.

Pakulski, G.

Palmer, R.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Parra-Cetina, J.

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

Patriarche, G.

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

Pérez-Serrano, A.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Perot lasers: the effect of spatial hole burning”, Opt. Express 19, 3284–3289 (2011).
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A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers”, Phys. Rev. A,  81, 043817 (2010).
[Crossref]

Peytavit, E.

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

Poingt, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Poitras, D.

Pommereau, F.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Poole, P.

Poole, P. J.

Prati, F.

Provost, J. G.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Quinlan, F.

Radovanovic, J.

Ramdane, A.

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

Raymond, S.

Regreny, P.

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]

Reithmaier, J. P.

A. C. O. Karni, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Coherent control in a semiconductor optical amplifier operating at room temperature,” Nat. Commun. 5, 5025 (2014).
[Crossref] [PubMed]

Renaudier, J.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Revin, D. G.

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Risken, H.

H. Risken and K. Nummedal, “Self pulsating in lasers,” J. App. Phys. 39, 4662–4672 (1968).
[Crossref]

Roelkens, G.

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]

Roldan, E.

Rösch, M.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Rossetti, M.

M. Rossetti, P. Bardella, and I. Montrosset, “Time-domain travelling-wave model for quantum dot passively mode-locked lasers,” IEEE J. Quantum Electron. 47, 139–150 (2011).
[Crossref]

Rousseau, B.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

Roy-Guay, D.

Sato, K.

K. Sato, “100 GHz optical pulse generation using Fabry-Perot laser under continuous wave operation,” Electron. Lett. 37, 763–764 (2001).
[Crossref]

Scalari, G.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Schmogrow, R.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Schneider, H.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Scholl, E.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Seyedi, M. A.

Shang, C.

Sichkovskyi, V.

A. C. O. Karni, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Coherent control in a semiconductor optical amplifier operating at room temperature,” Nat. Commun. 5, 5025 (2014).
[Crossref] [PubMed]

Silva, F.

Slight, T. J.

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Smit, M.K.

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

Sorel, M.

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Spuesens, T.

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]

Surre, F.

S. Latkowski, F. Surre, and P. Landais, “Terahertz wave generation from a DC-biased multimode laser,” App. Phys. Lett. 92, 081109 (2008).
[Crossref]

Tessmann, A.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Troccoli, M.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Van Thourhout, D.

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]

Villares, G.

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Vukovic, N.

Waldburger, D.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Wan, Y.

Wang, C. Y.

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Woggon, U.

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

Yilmaz, T.

Zhang, S. Y.

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Zhu, J.

H. Choi, V.-M. Gkortsas, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, F. Capasso, F. X. Kärtner, and T. B. Norris, “Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser,” Nat. Photonics 4, 706–711 (2010).
[Crossref]

Zwick, T.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

App. Phys. Lett. (2)

S. Latkowski, F. Surre, and P. Landais, “Terahertz wave generation from a DC-biased multimode laser,” App. Phys. Lett. 92, 081109 (2008).
[Crossref]

S. Latkowski, J. Parra-Cetina, R. Maldonado-Basilio, P. Landais, G. Ducournau, A. Beck, E. Peytavit, T. Akalin, and J.-F. Lampin, “Analysis of a narrowband terahertz signal generated by a unitravelling carrier photodiode coupled with a dual-mode semiconductor Fabry-Perot laser,” App. Phys. Lett. 96, 241106 (2010).
[Crossref]

App. Phys. Letters (1)

C. C. Nshii, C. N. Ironside, M. Sorel, T. J. Slight, S. Y. Zhang, D. G. Revin, and J. W. Cockburn, “A unidirectional quantum cascade ring laser,” App. Phys. Letters 97, 231107 (2010).
[Crossref]

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

K. Sato, “100 GHz optical pulse generation using Fabry-Perot laser under continuous wave operation,” Electron. Lett. 37, 763–764 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Rossetti, P. Bardella, and I. Montrosset, “Time-domain travelling-wave model for quantum dot passively mode-locked lasers,” IEEE J. Quantum Electron. 47, 139–150 (2011).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

M. Gioannini, P. Bardella, and I. Montrosset, “Time-domain traveling-wave analysis of the multimode dynamics of quantum dot Fabry-Perot lasers,” IEEE J. Sel. Top. Quantum Electron. 21, 698–708 (2015).
[Crossref]

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. v. 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 µ m,” IEEE J. Sel. Top. Quantum Electron. 13, 111–124 (2007).
[Crossref]

J. App. Phys. (1)

H. Risken and K. Nummedal, “Self pulsating in lasers,” J. App. Phys. 39, 4662–4672 (1968).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Nanophotonics (1)

J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, “Quantum cascade laser frequency combs,” Nanophotonics 5, 272–291 (2016).
[Crossref]

Nat. Commun. (2)

M. Kolarczik, N. Owschimikow, J. Korn, B. Lingnau, Y. Kaptan, D. Bimberg, E. Scholl, K. Lüdge, and U. Woggon, “Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature,” Nat. Commun. 4, 2953 (2013).
[Crossref] [PubMed]

A. C. O. Karni, G. Eisenstein, V. Sichkovskyi, V. Ivanov, and J. P. Reithmaier, “Coherent control in a semiconductor optical amplifier operating at room temperature,” Nat. Commun. 5, 5025 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

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]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

H. Choi, V.-M. Gkortsas, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, F. Capasso, F. X. Kärtner, and T. B. Norris, “Ultrafast Rabi flopping and coherent pulse propagation in a quantum cascade laser,” Nat. Photonics 4, 706–711 (2010).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Photon. Res. (1)

Phys. Rev. A (2)

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers”, Phys. Rev. A,  81, 043817 (2010).
[Crossref]

A. Gordon, C. Y. Wang, L. Diehl, F. X. Kärtner, A. Belyanin, D. Bour, S. Corzine, G. Höfler, H. C. Liu, H. Schneider, T. Maier, M. Troccoli, J. Faist, and F. Capasso, “Multimode regimes in quantum cascade lasers: From coherent instabilities to spatial hole burning,” Phys. Rev. A 77, 1–18 (2008).
[Crossref]

Proc. SPIEE (1)

L. L. Columbo, P. Bardella, M. Gioannini, and Politecnico di Torino (Italy), “Spontaneous generation of frequency combs in QD lasers,” Proc. SPIEE 10553, 105530 (2018).

Rev. Mod. Phys. (1)

T. W. Hänsch, “Nobel lecture: Passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

Science (2)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref] [PubMed]

Other (4)

Y. Barbarin, S. Anantathanasarn, E.A.J.M. Bente, Y.S. Oei, M.K. Smit, and R. Nötzel, “InAs/InP quantum dot Fabry-Perot and ring lasers in the 1.55 µ m range using deeply etched ridge waveguides,” Proceedings Symposium IEEE/LEOS Benelux Chapter, Eindhoven137–140 (2006).

N. Eiselt, H. Griesser, M. H. Eiselt, W. Kaiser, S. Aramideh, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Real-time 200 Gb/s (4×56.25 Gb/s) PAM-4 transmission over 80 km SSMF using quantum-dot laser and silicon ring-modulator,” in “Optical Fiber Communication Conference,” (2017), p. W4D.3.

J. Faist, Quantum Cascade Lasers, (Oxford University Press, 2013).
[Crossref]

L. Lugiato, F. Prati, and M. Brambilla, Nonlinear Optical Systems (Cambridge University, 2015).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Sketch of the unidirectional ring configuration. (b) Schematic of the electron dynamics in an exemplary quantum dot sub-group i (left). Effective gain lineshape corresponding to inhomogeneous gain broadening of ≃ 4 THz (≃ 16 meV) and ≃ 10 THz (≃ 40 meV). The the FWHM of the homogeneous gain linewidth is 2Γ ≃ 2.4 THz (≃ 10 meV) corresponding to a dipole dephasing time of 130 fs (right). The zero frequency in the x -axis corresponds to ω0/(2π).
Fig. 2
Fig. 2 Results of the LSA of the TW solutions for different bias currents. Plot of the parametric gain for each value of the frequency νz = ωz/2π = kz vg/2π treated as continuous variable.
Fig. 3
Fig. 3 Bifurcation diagram of the TW solutions: the maxima and minima in the output power time traces are reported against the bias current as control parameter. Red lines correspond to the TW solutions calculated using Eqs. (5)(8).
Fig. 4
Fig. 4 Temporal evolution of the output power (a,b), optical spectrum (c) and RF spectrum (d) obtained for a value of bias current of 75 mA. In panel (b) we report a space-time representation of the pulse dynamics for 75 mA. A long time trace is divided in intervals corresponding to the cold cavity round trip time τ = /c (indicated in panel (a)). These segments are then stacked on top of each other so that the horizontal axis is equivalent to space inside the cavity while the vertical dimension describes the evolution in units of round trips. The lowest frequency dashed line in panel (d) corresponds to the ring resonator FSR (equal to ≃ 440 GHz), while the other two dashed lines are integer multiple of it. The other parameters are those used in Fig. 2.
Fig. 5
Fig. 5 Temporal evolution of the output power (a,b), optical spectrum (c) and RF spectrum (d) obtained for a value of bias current of 95 mA. Dashed lines in panel (d) denote the first cold cavity modes. The other parameters are those used in Fig. 4.
Fig. 6
Fig. 6 Colour map representation of the frequency corresponding to the absolute maximum in the RF spectrum (ν ≠ 0), always close to νR, and the ratio between its amplitude and that of the highest side mode as a function of the cavity length L and the bias current I (a,b) or as a function of the degree of inhomogeneous broadening (number of populations) that ranges from a FWHM of ≃ 5.5 THz (≃22 meV) to a FWHM of ≃10.5 THz (≃42 meV) and the bias current I for a fixed cavity length L = 200 µm (c,d). The other parameters are those used in Fig. 4.
Fig. 7
Fig. 7 Temporal evolution of the output power (a,b), optical spectrum (c) and RF spectrum (d) obtained for a value of bias current of 75 mA. We consider 11 QDs populations whose central emission frequencies are again separated by a 1 THz. The other parameters are those used in Fig. 4.
Fig. 8
Fig. 8 Average values of the modal power and of the differential phase. The errors bars denote the standard deviation of their temporal fluctuations in the case of 3 (a), (c) and 11 populations (b), (d). The other parameters are those used in Fig. 4.
Fig. 9
Fig. 9 Results of the LSA of the TW solutions for I = 60 mA for a bidirectional ring configuration (a) and an unidirectional one (b). Plot of the parametric gain for each value of the frequency νz = ωz/2π = kz vg/2π treated as continuous variable. The other parameters are those used in Fig. 4.

Tables (1)

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Table 1 Main materials and device parameters used in the TDTW model.

Equations (18)

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E ( z , t ) t = γ p ( E z α w g L 2 E C i = N N G ¯ i p i + S s p ± )
p i ( z , t ) t = ( j δ i / Γ 1 ) p i D ( 2 ρ i 1 ) E
ρ i ( z , t ) t = ρ i γ e ( 1 ρ W L ) + F ρ W L γ C ( 1 ρ i ) γ s p ρ i 2 γ n r G S ρ i + H R e ( E * p i )
ρ W L ( z , t ) t = Λ τ d γ n r W L ρ W L + i = N N [ G ¯ i ρ W L γ C ( 1 ρ i ) + G ¯ i F ρ i γ e ( 1 ρ W L ) ] .
E E η Γ x y d G S Γ , p 0 , i G S j p 0 , i G S η Γ x y N D d G S 2 ϵ 0 Γ h Q D
C = ω 0 L Γ x , y μ 2 c η , D = d G S 2 N D ϵ 0 Γ h Q D , F = D W L μ N D , H = τ s p Γ 2 ω 0 Γ x y ϵ 0 h Q D η ω i G S d G S 2 N D
E ( 0 , t ) = 1 k 2 E ( L , t ) ,
E = E ¯ e j ( δ ω / Γ t δ k L z ) , p i = p ¯ i e j ( δ ω / Γ t δ k L z ) ρ i = ρ i ¯ , ρ W L = ρ W L ¯
ρ i ¯ = [ D ( 2 ρ i ¯ 1 ) E ¯ ] j δ i / Γ 1 j δ ω / Γ
ρ W L ¯ = Λ τ d + 1 F i = N N G ¯ i ρ i ¯ γ e γ n r W L + i = N N G ¯ i γ C ( 1 ρ i ¯ ) + 1 F i = N N G ¯ i ρ i ¯ γ e
0 = E ¯ ( α w g L 2 + C D i = N N G ¯ i ( 2 ρ i ¯ , 1 ) j δ i / Γ 1 j δ ω / Γ )
0 = ρ i ¯ γ e ( 1 ρ W L ¯ ) + F ρ W L ¯ γ C ( 1 ρ i ¯ ) γ s p ρ i ¯ 2 + H D R e ( | E ¯ | 2 ( 2 ρ i ¯ 1 ) j δ i / Γ 1 j δ ω / Γ ) ,
ν R , i = ( γ s p H D 2 | E | 2 + ( ( δ i δ ω ) / Γ ) 2 ) 0.5 / 2 π .
E = ( E ¯ + δ E ) e j ( δ ω / Γ t δ k L z ) p i = ( p ¯ i + δ p i ) e j ( δ ω / Γ t δ k L z ) ρ W L ( z , t ) = ρ W L ¯ + δ ρ W L ρ i ( z , t ) = p ¯ i + δ ρ i
δ E t + γ p δ E z = γ p ( α w g L 2 δ E C i = N N G ¯ i δ p i )
δ p i ( z , t ) t = ( j δ i / Γ 1 j δ ω / Γ ) δ p i D ( 2 δ ρ i ) E D ( 2 ρ i 1 ) δ E
δ ρ i ( z , t ) t = δ ρ i γ e ( 1 ρ W L ) + ρ i δ ρ W L γ e F δ ρ i ρ W L γ C + F ( 1 ρ i ) δ ρ W L γ C 2 ρ i δ ρ i + H R e ( δ E * p i + E * δ p i )
δ ρ W L ( z , t ) t = δ ρ W L γ n r W L + i = N N [ G ¯ i δ ρ W L γ C ( 1 ρ i ) + G ¯ i ρ W L γ C δ ρ i + G ¯ i F δ ρ i γ e ( 1 ρ W L ) G ¯ i F ρ i γ e δ ρ W L ] .

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