Abstract

The linewidth enhancement factor α is a key parameter determining the spectral and dynamical behavior of semiconductor lasers. Here, we propose and demonstrate a method for determining this parameter based on a direct measurement of variations in the laser gain and emission spectrum when subject to delayed optical feedback. We then use our approach to determine the pump current dependent linewidth enhancement factor of a high-β quantum dot micropillar laser. The validity of our approach is confirmed comparing it to two conventional methods, one based on the comparison of the linewidths above and below threshold and the other based on injection locking properties. Furthermore, the pump power dependence of α is quantitatively described by simulations based on a quantum-optical model.

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

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    [Crossref]
  27. C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 um ingaasp semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152–1156 (1985).
    [Crossref]
  28. S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
    [Crossref] [PubMed]
  29. R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J. Light. Technol. 4, 1655–1661 (1986).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  36. W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37, 109–184 (2013).
    [Crossref]
  37. W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. Appl. 3, e201 (2014).
    [Crossref]
  38. M. Lorke, F. Jahnke, and W. W. Chow, “Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers,” Appl. Phys. Lett. 90, 3–5 (2007).
    [Crossref]
  39. G. Giuliani, S. Donati, and W. Elsässer, “Measurement of linewidth enhancement factor variations in external cavity semiconductor lasers,” EQEC ’05.” Eur. Quantum Electron. Conf. 2005.  25, 13 (2005).
    [Crossref]
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  41. S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
    [Crossref]

2018 (3)

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
[Crossref] [PubMed]

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

2016 (5)

W. E. Hayenga, H. Garcia-Gracia, H. Hodaei, C. Reimer, R. Morandotti, P. LiKamWa, and M. Khajavikhan, “Second-order coherence properties of metallic nanolasers,” Optica 3, 1187–1193 (2016).
[Crossref]

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

2015 (1)

A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
[Crossref]

2014 (2)

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µ m distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105, 131112 (2014).
[Crossref]

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. Appl. 3, e201 (2014).
[Crossref]

2013 (1)

W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37, 109–184 (2013).
[Crossref]

2012 (2)

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201 (2012).
[Crossref]

A. Consoli, B. Bonilla, J. M. G. Tijero, and I. Esquivias, “Self-validating technique for the measurement of the linewidth enhancement factor in semiconductor lasers,” Opt. Express 20, 4979–4987 (2012).
[Crossref] [PubMed]

2010 (1)

2008 (1)

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

2007 (2)

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43, 6–15 (2007).
[Crossref]

M. Lorke, F. Jahnke, and W. W. Chow, “Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers,” Appl. Phys. Lett. 90, 3–5 (2007).
[Crossref]

2006 (1)

G. Giuliani, S. Donati, and W. Elsässer, “Measurement of linewidth enhancement factor of different semiconductor lasers in operating conditions,” Proc. SPIE 6184, 61841D (2006).

2005 (2)

A. Villafranca, J. A. Lazaro, I. Salinas, and I. Garces, “Measurement of the linewidth enhancement factor in dfb lasers using a high-resolution optical spectrum analyzer,” IEEE Photonics Technol. Lett. 17, 2268–2270 (2005).
[Crossref]

G. Giuliani, S. Donati, and W. Elsässer, “Measurement of linewidth enhancement factor variations in external cavity semiconductor lasers,” EQEC ’05.” Eur. Quantum Electron. Conf. 2005.  25, 13 (2005).
[Crossref]

2004 (1)

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photonics Technol. Lett. 16, 990–992 (2004).
[Crossref]

2001 (1)

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photonics Technol. Lett. 13, 430–432 (2001).
[Crossref]

2000 (1)

P. P. Vasil’ev, I. H. White, and J. Gowar, “Fast phenomena in semiconductor lasers,” Rep. Prog. Phys. 63, 1997–2042 (2000).
[Crossref]

1997 (1)

J. Jeong and Y. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33, 605–606 (1997).
[Crossref]

1996 (1)

Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

1994 (1)

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

1993 (1)

Y. Sorel and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Light. Technol. 11, 1937–1940 (1993).
[Crossref]

1992 (1)

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28, 9–11 (1992).
[Crossref]

1990 (1)

R. Hui, A. Mecozzi, A. D’Ottavi, and P. Spano, “Novel measurement technique of alpha factor in dfb semiconductor lasers by injection locking,” Electron. Lett. 26, 997–998 (1990).
[Crossref]

1988 (1)

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247 (1988).
[Crossref]

1987 (1)

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–an overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[Crossref]

1986 (1)

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J. Light. Technol. 4, 1655–1661 (1986).
[Crossref]

1985 (2)

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 um ingaasp semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152–1156 (1985).
[Crossref]

M. Osiński, D. Gallagher, and I. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

1983 (2)

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19, 927–929 (1983).
[Crossref]

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[Crossref]

1982 (2)

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[Crossref]

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[Crossref]

1981 (1)

M. W. Fleming and A. Mooradian, “Fundamental line broadening of single-mode (GaAl)As diode lasers,” Appl. Phys. Lett. 38, 511–513 (1981).
[Crossref]

1958 (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[Crossref]

Barzel, R.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Beyer, J.

Bimberg, D.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Birocheau, C.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28, 9–11 (1992).
[Crossref]

Björk, G.

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Böckler, C.

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

Bonilla, B.

Butté, R.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Buus, J.

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–an overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[Crossref]

Callsen, G.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Carlin, J.-F.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Carmele, A.

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

Carras, M.

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µ m distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105, 131112 (2014).
[Crossref]

Chow, W. W.

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. Appl. 3, e201 (2014).
[Crossref]

W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37, 109–184 (2013).
[Crossref]

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201 (2012).
[Crossref]

M. Lorke, F. Jahnke, and W. W. Chow, “Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers,” Appl. Phys. Lett. 90, 3–5 (2007).
[Crossref]

Chraplyvy, A.

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J. Light. Technol. 4, 1655–1661 (1986).
[Crossref]

Chuang, S. L.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photonics Technol. Lett. 13, 430–432 (2001).
[Crossref]

Claudon, J.

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

Collins, J. V.

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19, 927–929 (1983).
[Crossref]

Consoli, A.

D’Ottavi, A.

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C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
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B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
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A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
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S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
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[Crossref]

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
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G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photonics Technol. Lett. 13, 430–432 (2001).
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C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

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S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
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M. Lorke, F. Jahnke, and W. W. Chow, “Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers,” Appl. Phys. Lett. 90, 3–5 (2007).
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Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
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S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
[Crossref] [PubMed]

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201 (2012).
[Crossref]

Maaßdorf, A.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

McInerney, J.

Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

Mecozzi, A.

R. Hui, A. Mecozzi, A. D’Ottavi, and P. Spano, “Novel measurement technique of alpha factor in dfb semiconductor lasers by injection locking,” Electron. Lett. 26, 997–998 (1990).
[Crossref]

Michel, F.

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

Mooradian, A.

M. W. Fleming and A. Mooradian, “Fundamental line broadening of single-mode (GaAl)As diode lasers,” Appl. Phys. Lett. 38, 511–513 (1981).
[Crossref]

Morandotti, R.

Morgan, R.

Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

Musial, A.

A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
[Crossref]

Olsson, N.

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 um ingaasp semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152–1156 (1985).
[Crossref]

Osinski, M.

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–an overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[Crossref]

M. Osiński, D. Gallagher, and I. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

Owschimikow, N.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Park, Y.

J. Jeong and Y. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33, 605–606 (1997).
[Crossref]

Pawlus, R.

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

Petermann, K.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247 (1988).
[Crossref]

Pohl, U. W.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Poole, P. J.

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

Porte, X.

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
[Crossref] [PubMed]

Redlich, C.

Reimer, C.

Reitzenstein, S.

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
[Crossref] [PubMed]

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
[Crossref]

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

Rosales, R.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Rousseau, I. M.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Salinas, I.

A. Villafranca, J. A. Lazaro, I. Salinas, and I. Garces, “Measurement of the linewidth enhancement factor in dfb lasers using a high-resolution optical spectrum analyzer,” IEEE Photonics Technol. Lett. 17, 2268–2270 (2005).
[Crossref]

Sarmiento, T.

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[Crossref]

Schires, K.

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µ m distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105, 131112 (2014).
[Crossref]

Schlottmann, E.

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

Schmidt, M.

Schneider, C.

S. Holzinger, C. Redlich, B. Lingnau, M. Schmidt, M. von Helversen, J. Beyer, C. Schneider, M. Kamp, S. Höfling, K. Lüdge, X. Porte, and S. Reitzenstein, “Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback,” Opt. Express 26, 22457–22470 (2018).
[Crossref] [PubMed]

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
[Crossref]

Schöll, E.

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201 (2012).
[Crossref]

Schulze, J.-H.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Schunk, N.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247 (1988).
[Crossref]

Shambat, G.

Sorel, Y.

Y. Sorel and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Light. Technol. 11, 1937–1940 (1993).
[Crossref]

Spano, P.

R. Hui, A. Mecozzi, A. D’Ottavi, and P. Spano, “Novel measurement technique of alpha factor in dfb semiconductor lasers by injection locking,” Electron. Lett. 26, 997–998 (1990).
[Crossref]

Strauß, M.

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

Strittmatter, A.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Tijero, J. M. G.

Tkach, R.

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J. Light. Technol. 4, 1655–1661 (1986).
[Crossref]

Toffano, Z.

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28, 9–11 (1992).
[Crossref]

Townes, C. H.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[Crossref]

Triviño, N. V.

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Vahala, K.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[Crossref]

Vasil’ev, P. P.

P. P. Vasil’ev, I. H. White, and J. Gowar, “Fast phenomena in semiconductor lasers,” Rep. Prog. Phys. 63, 1997–2042 (2000).
[Crossref]

Villafranca, A.

A. Villafranca, J. A. Lazaro, I. Salinas, and I. Garces, “Measurement of the linewidth enhancement factor in dfb lasers using a high-resolution optical spectrum analyzer,” IEEE Photonics Technol. Lett. 17, 2268–2270 (2005).
[Crossref]

von Helversen, M.

Vuckovic, J.

Wang, C.

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

Weyers, M.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

White, I.

M. Osiński, D. Gallagher, and I. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

White, I. H.

P. P. Vasil’ev, I. H. White, and J. Gowar, “Fast phenomena in semiconductor lasers,” Rep. Prog. Phys. 63, 1997–2042 (2000).
[Crossref]

Woggon, U.

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

Wolters, J.

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

Wright, M.

Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

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G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Yariv, A.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[Crossref]

Yu, Y.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photonics Technol. Lett. 16, 990–992 (2004).
[Crossref]

AIP Adv (1)

L. Jumpertz, F. Michel, R. Pawlus, W. Elsässer, K. Schires, M. Carras, and F. Grillot, “Measurements of the linewidth enhancement factor of mid-infrared quantum cascade lasers by different optical feedback techniques,” AIP Adv.  6, 015212 (2016).
[Crossref]

Appl. Phys. Lett (2)

B. Herzog, B. Lingnau, M. Kolarczik, Y. Kaptan, D. Bimberg, A. Maaßdorf, U. W. Pohl, R. Rosales, J.-H. Schulze, A. Strittmatter, M. Weyers, U. Woggon, K. Lüdge, and N. Owschimikow, “Strong amplitude-phase coupling in submonolayer quantum dots,” Appl. Phys. Lett.  109, 201102 (2016).
[Crossref]

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett.  92, 091107 (2008).
[Crossref]

Appl. Phys. Lett. (4)

L. Jumpertz, M. Carras, K. Schires, and F. Grillot, “Regimes of external optical feedback in 5.6 µ m distributed feedback mid-infrared quantum cascade lasers,” Appl. Phys. Lett. 105, 131112 (2014).
[Crossref]

M. Lorke, F. Jahnke, and W. W. Chow, “Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers,” Appl. Phys. Lett. 90, 3–5 (2007).
[Crossref]

M. W. Fleming and A. Mooradian, “Fundamental line broadening of single-mode (GaAl)As diode lasers,” Appl. Phys. Lett. 38, 511–513 (1981).
[Crossref]

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[Crossref]

Electron. Lett. (5)

M. Osiński, D. Gallagher, and I. White, “Measurement of linewidth broadening factor in gain-switched InGaAsP injection lasers by CHP method,” Electron. Lett. 21, 981–982 (1985).
[Crossref]

R. Hui, A. Mecozzi, A. D’Ottavi, and P. Spano, “Novel measurement technique of alpha factor in dfb semiconductor lasers by injection locking,” Electron. Lett. 26, 997–998 (1990).
[Crossref]

I. D. Henning and J. V. Collins, “Measurements of the semiconductor laser linewidth broadening factor,” Electron. Lett. 19, 927–929 (1983).
[Crossref]

Z. Toffano, A. Destrez, C. Birocheau, and L. Hassine, “New linewidth enhancement determination method in semiconductor lasers based on spectrum analysis above and below threshold,” Electron. Lett. 28, 9–11 (1992).
[Crossref]

J. Jeong and Y. Park, “Accurate determination of transient chirp parameter in high speed digital lightwave transmitters,” Electron. Lett. 33, 605–606 (1997).
[Crossref]

EQEC ’05.” Eur. Quantum Electron. Conf. 2005 (1)

G. Giuliani, S. Donati, and W. Elsässer, “Measurement of linewidth enhancement factor variations in external cavity semiconductor lasers,” EQEC ’05.” Eur. Quantum Electron. Conf. 2005.  25, 13 (2005).
[Crossref]

IEEE J. Quantum Electron. (7)

R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J. Quantum Electron. 18, 976–983 (1982).
[Crossref]

Hua Li, T. Lucas, J. McInerney, M. Wright, and R. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

C. Henry, N. Olsson, and N. Dutta, “Locking range and stability of injection locked 1.54 um ingaasp semiconductor lasers,” IEEE J. Quantum Electron. 21, 1152–1156 (1985).
[Crossref]

T. Fordell and A. M. Lindberg, “Experiments on the linewidth-enhancement factor of a vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 43, 6–15 (2007).
[Crossref]

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24, 1242–1247 (1988).
[Crossref]

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[Crossref]

M. Osinski and J. Buus, “Linewidth broadening factor in semiconductor lasers–an overview,” IEEE J. Quantum Electron. 23, 9–29 (1987).
[Crossref]

IEEE Photonics Technol. Lett. (3)

A. Villafranca, J. A. Lazaro, I. Salinas, and I. Garces, “Measurement of the linewidth enhancement factor in dfb lasers using a high-resolution optical spectrum analyzer,” IEEE Photonics Technol. Lett. 17, 2268–2270 (2005).
[Crossref]

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photonics Technol. Lett. 16, 990–992 (2004).
[Crossref]

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photonics Technol. Lett. 13, 430–432 (2001).
[Crossref]

J. Light. Technol. (2)

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-um distributed feedback lasers,” J. Light. Technol. 4, 1655–1661 (1986).
[Crossref]

Y. Sorel and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Light. Technol. 11, 1937–1940 (1993).
[Crossref]

Light Sci. Appl. (1)

S. Kreinberg, T. Grbešić, M. Strauß, A. Carmele, M. Emmerling, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-optical spectroscopy of a two-level system using an electrically driven micropillar laser as a resonant excitation source, Light Sci. Appl. 7, 41 (2018).
[Crossref]

Light. Sci. Appl. (1)

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. Appl. 3, e201 (2014).
[Crossref]

Nat. Commun. (1)

S. T. Jagsch, N. V. Triviño, F. Lohof, G. Callsen, S. Kalinowski, I. M. Rousseau, R. Barzel, J.-F. Carlin, F. Jahnke, R. Butté, C. Gies, A. Hoffmann, N. Grandjean, and S. Reitzenstein, “A quantum optical study of thresholdless lasing features in high-β nitride nanobeam cavities,” Nat. Commun. 9, 564 (2018).
[Crossref]

Opt. Express (3)

Optica (1)

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
[Crossref]

Phys. Rev. A (1)

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Phys. Rev. Appl (1)

E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, and J. Wolters, andS.Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.  6, 044023 (2016).
[Crossref]

Phys. Rev. B (1)

A. Musiał, C. Hopfmann, T. Heindel, C. Gies, M. Florian, H. A. M. Leymann, A. Foerster, C. Schneider, F. Jahnke, S. Höfling, M. Kamp, and S. Reitzenstein, “Correlations between axial and lateral emission of coupled quantum dot–micropillar cavities,” Phys. Rev. B 91, 205310 (2015).
[Crossref]

Phys. Rev. E (1)

B. Lingnau, K. Lüdge, W. W. Chow, and E. Schöll, “Failure of the α factor in describing dynamical instabilities and chaos in quantum-dot lasers,” Phys. Rev. E 86, 065201 (2012).
[Crossref]

Proc. SPIE (1)

G. Giuliani, S. Donati, and W. Elsässer, “Measurement of linewidth enhancement factor of different semiconductor lasers in operating conditions,” Proc. SPIE 6184, 61841D (2006).

Prog. Quantum Electron. (1)

W. W. Chow and F. Jahnke, “On the physics of semiconductor quantum dots for applications in lasers and quantum optics,” Prog. Quantum Electron. 37, 109–184 (2013).
[Crossref]

Rep. Prog. Phys. (1)

P. P. Vasil’ev, I. H. White, and J. Gowar, “Fast phenomena in semiconductor lasers,” Rep. Prog. Phys. 63, 1997–2042 (2000).
[Crossref]

Sci. Rep. (1)

C. Wang, K. Schires, M. Osiński, P. J. Poole, and F. Grillot, “Thermally insensitive determination of the linewidth broadening factor in nanostructured semiconductor lasers using optical injection locking,” Sci. Rep. 6, 27825 (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Sketch of the experimental setup. The QD-micropillar laser is mounted inside a He-flow cryostat and is stabilized at a temperature of T = 32.00 ± 0.01 K. Optical feedback is applied to its axial emission. The spectral properties are measured with charge-coupled devices (CCD) in both the axial and lateral directions. High-resolution spectra are acquired with a Fabry-Perot interferometer (FPI) in the axial direction.
Fig. 2
Fig. 2 (a) Exemplary high-resolution emission spectra of a QD micropillar showing the feedback-induced shift of the lasing mode at I = 1.9 Ith. (b) Extracted modal gain as a function of the pump current with and without optical feedback (FB). The inset depicts spectra of the QD emission measured in lateral detection. The shaded gray area represents the integration range of the gain contributing to the lasing mode.
Fig. 3
Fig. 3 Emission linewidth plotted as a function of the inverse optical output power (measured with a powermeter). The α-factor can be determined from linear fits (dashed lines) of the linewidths above (see inset) and below threshold.
Fig. 4
Fig. 4 Determining α from injection locking. Normalized intensity of the frequency-locked oscillation as a function of detuning Δ between the master laser and slave microlaser for different pump currents (a) I = 1.5 Ith and (b) I = 1.7 Ith. Solid lines indicate the edge of the locking cones.
Fig. 5
Fig. 5 Pump current dependence of the α-factor. The proposed method (green triangles), theory (orange circles), injection locking (blue triangles) and the Schawlow-Townes-like law (dashed grey line) are compared. The input-output characteristic (right axis, red and black dots for feedback and no-feedback scenarios, respectively) are plotted as references.

Equations (8)

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α = Δ n Δ n = 4 π Δ ν Δ G ,
κ = 2 π ν 0 Q = 105.62 ns 1 ,
Δ ν = Δ ν 0 + ζ P ,
α = 2 ζ > ζ < 1 ,
C K e f f 1 + α 2 < ν l o c k i n g < C K e f f ,
α = ( m m + ) 2 1 ,
K δ n ( ω ) + i g ( ω ) = ω ε 0 n b g c w E ( ω ) i , j μ i j p i j ( ω )
d d t p i j = i ω i j p i j + i Ω i j ( 1 n i e n j h ) + S i j c c + S i j c p ,

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