Abstract

This Letter presents the results revealing the influence of external optical feedback (EOF) on the alpha factor, or the linewidth enhancement factor, of semiconductor lasers operating on single mode. First, a method is proposed for the measurement of the alpha over a wide range of optical feedback level, which provides an effective way for investigating the dependence of the alpha on laser operating conditions. Second, experimental investigation based on the proposed method is performed on a GaAlAs laser diode with a multiquantum well structure. It is discovered that the alpha value remains approximately constant with increasing injection current, but has a strong dependence on EOF.

© 2013 Optical Society of America

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  2. M. Osiniski and J. Buus, IEEE J. Quantum Electron. 23, 9 (1987).
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  7. F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
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    [CrossRef]
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  18. Y. Yu, J. Xi, and J. Chicharo, Opt. Express 19, 9582 (2011).
    [CrossRef]
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    [CrossRef]

2012

2011

2008

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

2007

T. Fordell and A. M. Lindberg, IEEE J. Quantum Electron. 43, 6 (2007).
[CrossRef]

Z. Mi and P. Bhattacharya, IEEE J. Quantum Electron. 43, 363 (2007).
[CrossRef]

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

2006

2005

E. Gehriga and O. Hess, Appl. Phys. Lett. 86, 203116 (2005).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

2004

Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
[CrossRef]

1987

M. Osiniski and J. Buus, IEEE J. Quantum Electron. 23, 9 (1987).
[CrossRef]

1984

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

1982

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

1980

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Acket, G.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Bhattacharya, P.

Z. Mi and P. Bhattacharya, IEEE J. Quantum Electron. 43, 363 (2007).
[CrossRef]

Bonilla, B.

Bosch, T.

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

T. Bosch, in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2004), pp. 385–392.

Buus, J.

M. Osiniski and J. Buus, IEEE J. Quantum Electron. 23, 9 (1987).
[CrossRef]

Chicharo, J.

Y. Fan, Y. Yu, J. Xi, and J. Chicharo, Appl. Opt. 50, 5064 (2011).
[CrossRef]

Y. Yu, J. Xi, and J. Chicharo, Opt. Express 19, 9582 (2011).
[CrossRef]

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

Consoli, A.

Dagens, B.

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

Den Boef, A.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Donati, S.

Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
[CrossRef]

Erasme, D.

Esquivias, I.

Fan, Y.

Fordell, T.

T. Fordell and A. M. Lindberg, IEEE J. Quantum Electron. 43, 6 (2007).
[CrossRef]

Gehriga, E.

E. Gehriga and O. Hess, Appl. Phys. Lett. 86, 203116 (2005).
[CrossRef]

Giuliani, G.

Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
[CrossRef]

Grillot, F.

K. Kechaou, F. Grillot, J. -G. Provost, B. Thedrez, and D. Erasme, Opt. Express 20, 26062 (2012).
[CrossRef]

G.-J. Provost and F. Grillot, IEEE J. Photon. 3, 476 (2011).
[CrossRef]

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

Hess, O.

E. Gehriga and O. Hess, Appl. Phys. Lett. 86, 203116 (2005).
[CrossRef]

Huyet, G.

Kechaou, K.

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Lenstra, D.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Lester, L. F.

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

Lin, C.-Y.

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

Lindberg, A. M.

T. Fordell and A. M. Lindberg, IEEE J. Quantum Electron. 43, 6 (2007).
[CrossRef]

Manuel, J.

Melnik, S.

Mi, Z.

Z. Mi and P. Bhattacharya, IEEE J. Quantum Electron. 43, 363 (2007).
[CrossRef]

Naderi, N. A.

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

Osiniski, M.

M. Osiniski and J. Buus, IEEE J. Quantum Electron. 23, 9 (1987).
[CrossRef]

Pochet, M.

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

Provost, G.-J.

G.-J. Provost and F. Grillot, IEEE J. Photon. 3, 476 (2011).
[CrossRef]

Provost, J. -G.

Provost, J.-G.

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

Su, H.

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

Thedrez, B.

Tijero, G.

Uskov, A.

Verbeek, B.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Xi, J.

Y. Fan, Y. Yu, J. Xi, and J. Chicharo, Appl. Opt. 50, 5064 (2011).
[CrossRef]

Y. Yu, J. Xi, and J. Chicharo, Opt. Express 19, 9582 (2011).
[CrossRef]

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

Yu, Y.

Y. Yu, J. Xi, and J. Chicharo, Opt. Express 19, 9582 (2011).
[CrossRef]

Y. Fan, Y. Yu, J. Xi, and J. Chicharo, Appl. Opt. 50, 5064 (2011).
[CrossRef]

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

F. Grillot, N. A. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, Appl. Phys. Lett. 93, 191108 (2008).
[CrossRef]

E. Gehriga and O. Hess, Appl. Phys. Lett. 86, 203116 (2005).
[CrossRef]

IEEE J. Photon.

G.-J. Provost and F. Grillot, IEEE J. Photon. 3, 476 (2011).
[CrossRef]

IEEE J. Quantum Electron.

Z. Mi and P. Bhattacharya, IEEE J. Quantum Electron. 43, 363 (2007).
[CrossRef]

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

M. Osiniski and J. Buus, IEEE J. Quantum Electron. 23, 9 (1987).
[CrossRef]

T. Fordell and A. M. Lindberg, IEEE J. Quantum Electron. 43, 6 (2007).
[CrossRef]

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
[CrossRef]

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

J. Xi, Y. Yu, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 41, 1058 (2005).
[CrossRef]

Y. Yu, J. Xi, J. Chicharo, and T. Bosch, IEEE J. Quantum Electron. 43, 527 (2007).
[CrossRef]

F. Grillot, B. Dagens, J.-G. Provost, H. Su, and L. F. Lester, IEEE J. Quantum Electron. 44, 946 (2008).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
[CrossRef]

Opt. Express

Other

T. Bosch, in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2004), pp. 385–392.

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Figures (2)

Fig. 1.
Fig. 1.

Influence of feedback parameter C on alpha factor.

Fig. 2.
Fig. 2.

Relationship between injection current and alpha.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ϕF(t)=ϕ0(t)C·sin[ϕF(t)+arctan(α)],
g(t)=cos(ϕF(t)),
p(t)=p0[1+m·g(t)],
ϕF(t)=ϕ0(t)+k1ϕ1(t)+k2ϕ2(t),
α=k2k1andC=k1+k2.
ΦF(f)=Φ0(f)+k1Φ1(f)+k2Φ2(f),
ΦF(f)=k1Φ1(f)+k2Φ2(f),wherefΩ.
ΨF=k1Ψ1+k2Ψ2,
k1=ΨFIΨ2RΨFRΨ2IΨ1IΨ2RΨ1RΨ2Iandk2=ΨFRΨ1IΨRIΨ1RΨ1IΨ2RΨ1RΨ2I,

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