Abstract

The stability of an optically injected laser is considered theoretically with an emphasis on the understanding of the locked phase whereas previous works focus primarily on the frequency detuning limits. Exemplary photon and carrier number curves for regions within and outside stable locking are presented. The dependence of the phase limits on injection ratio naturally divides into three regions with qualitatively different descriptions for the phase boundaries in each. Frequency detunings at which the locked phase is zero for different injection ratios are investigated. Using this zero phase point it is shown that the coupling rate between the injected and internal field as well as the linewidth enhancement factor can be determined in a single voltage measurement under weak injection. The modulation response parameters at these detunings are analysed and shown to be strongly interconnected.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  25. P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked vcsels,” Opt. Express20, 6980–6988 (2012).
    [CrossRef] [PubMed]
  26. S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
    [CrossRef]
  27. S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
    [CrossRef]
  28. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., 1995).
  29. S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
    [CrossRef]

2012 (5)

2011 (1)

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

2009 (1)

E. Lau and M. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Topics Quantum Electron.15, 618–633 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (3)

N. M. Al-Hosiny, I. Henning, and M. Adams, “Correlation of electron density changes with optical frequency shifts in optically injected semiconductor lasers,” IEEE J. Quantum Electron.42, 570–580 (2006).
[CrossRef]

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[CrossRef]

P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proc. IEEE94, 952–985 (2006).
[CrossRef]

2005 (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

2004 (1)

S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[CrossRef]

2003 (2)

Y. Okajima, S. Hwang, and J. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003).
[CrossRef]

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39, 1196–1204 (2003).
[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 Photon. Technol. Lett.13, 430–432 (2001).
[CrossRef]

2000 (1)

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

1996 (2)

T. B. Simpson, J. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron.32, 1456–1468 (1996).
[CrossRef]

H. Li, T. Lucas, J. G. 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]

1992 (2)

M. Van Exter and J. Woerdman, “Determination of alpha factor of Fabry-Perot-type semiconductor laser by injection locking,” Electron. Lett.28, 1607–1608 (1992).
[CrossRef]

K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992).
[CrossRef] [PubMed]

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]

1985 (2)

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

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron.21, 784–793 (1985).
[CrossRef]

1982 (1)

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

Adams, M.

N. M. Al-Hosiny, I. Henning, and M. Adams, “Correlation of electron density changes with optical frequency shifts in optically injected semiconductor lasers,” IEEE J. Quantum Electron.42, 570–580 (2006).
[CrossRef]

Al-Hosiny, N. M.

N. M. Al-Hosiny, I. Henning, and M. Adams, “Correlation of electron density changes with optical frequency shifts in optically injected semiconductor lasers,” IEEE J. Quantum Electron.42, 570–580 (2006).
[CrossRef]

Amann, M.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Atsuki, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39, 1196–1204 (2003).
[CrossRef]

Barrios, P.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Besnard, P.

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

Bhardwaj, A.

Bloch, E.

Bogris, A.

Bondiou, M.

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

Caballero, J.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Champneys, A. R.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Chan, S.-C.

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

Chang-Hasnain, C.

E. K. Lau, X. Zhao, H.-K. Sung, D. Parekh, C. Chang-Hasnain, and M. C. Wu, “Strong optical injection-locked semiconductor lasers demonstrating > 100-GHz resonance frequencies and 80-GHz intrinsic bandwidths,” Opt. Express16, 6609–6618 (2008).
[CrossRef] [PubMed]

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[CrossRef]

Chang-Hasnain, C. J.

P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked vcsels,” Opt. Express20, 6980–6988 (2012).
[CrossRef] [PubMed]

X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett.20, 395–397 (2008).
[CrossRef]

Chen, Z.

Chow, W.

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[CrossRef]

Chrostowski, L.

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[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 Photon. Technol. Lett.13, 430–432 (2001).
[CrossRef]

Coldren, L. A.

Corbett, B.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., 1995).

D’Ottavi, 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]

Daly, A.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Doedel, E. J.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Dutta, N.

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

Essiambre, R.

P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proc. IEEE94, 952–985 (2006).
[CrossRef]

Fairgrieve, T.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Fragkos, A.

Gabet, R.

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

Gavrielides, A.

T. B. Simpson, J. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron.32, 1456–1468 (1996).
[CrossRef]

Griffith, Z.

Gründl, T.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Guo, P.

Hayashi, K.

K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992).
[CrossRef] [PubMed]

Henning, I.

N. M. Al-Hosiny, I. Henning, and M. Adams, “Correlation of electron density changes with optical frequency shifts in optically injected semiconductor lasers,” IEEE J. Quantum Electron.42, 570–580 (2006).
[CrossRef]

Henry, C.

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

Hsieh, S.-C.

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

Huber, S.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Hui, R.

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]

Hwang, S.

Y. Okajima, S. Hwang, and J. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003).
[CrossRef]

Hwang, S. K.

S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[CrossRef]

Hwang, S.-K.

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

Ida, Y.

K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992).
[CrossRef] [PubMed]

Iiyama, K.

K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992).
[CrossRef] [PubMed]

Jacobsen, G.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron.21, 784–793 (1985).
[CrossRef]

Jiao, Z.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Jin, X.

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

Johansson, L. A.

Kawashima, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39, 1196–1204 (2003).
[CrossRef]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

Kuznetsov, Y.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Lang, R.

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

Lau, E.

E. Lau and M. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Topics Quantum Electron.15, 618–633 (2009).
[CrossRef]

Lau, E. K.

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

Li, C.-Y.

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

Li, H.

H. Li, T. Lucas, J. G. 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]

Liu, G.

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

Liu, J.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[CrossRef]

Y. Okajima, S. Hwang, and J. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003).
[CrossRef]

T. B. Simpson, J. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron.32, 1456–1468 (1996).
[CrossRef]

Lu, M.

Lu, Z.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Lucas, T.

H. Li, T. Lucas, J. G. 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]

McInerney, J. G.

H. Li, T. Lucas, J. G. 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]

Mogensen, F.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron.21, 784–793 (1985).
[CrossRef]

Morgan, R.

H. Li, T. Lucas, J. G. 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]

Müller, M.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Murakami, A.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39, 1196–1204 (2003).
[CrossRef]

Okajima, Y.

Y. Okajima, S. Hwang, and J. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003).
[CrossRef]

Oldeman, B.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Olesen, H.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron.21, 784–793 (1985).
[CrossRef]

Olsson, N.

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

Paffenroth, R.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Pakulski, G.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Parekh, D.

Park, H.

Phelan, R.

Poitras, D.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Poole, P.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Rodwell, M. J.

Roycroft, B.

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

Sandstede, B.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

T. B. Simpson, J. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron.32, 1456–1468 (1996).
[CrossRef]

Sivananthan, A.

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]

Stéphan, G. M.

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

Sung, H.-K.

Syvridis, D.

Van Exter, M.

M. Van Exter and J. Woerdman, “Determination of alpha factor of Fabry-Perot-type semiconductor laser by injection locking,” Electron. Lett.28, 1607–1608 (1992).
[CrossRef]

Wang, X.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

White, J. K.

S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[CrossRef]

Wieczorek, S.

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[CrossRef]

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

Winzer, P.

P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proc. IEEE94, 952–985 (2006).
[CrossRef]

Woerdman, J.

M. Van Exter and J. Woerdman, “Determination of alpha factor of Fabry-Perot-type semiconductor laser by injection locking,” Electron. Lett.28, 1607–1608 (1992).
[CrossRef]

Wright, M.

H. Li, T. Lucas, J. G. 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]

Wu, M.

E. Lau and M. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Topics Quantum Electron.15, 618–633 (2009).
[CrossRef]

Wu, M. C.

Xu, A.

Yang, W.

Zhang, C.

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

Zhang, X.

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Zhao, X.

Electron. Lett. (2)

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]

M. Van Exter and J. Woerdman, “Determination of alpha factor of Fabry-Perot-type semiconductor laser by injection locking,” Electron. Lett.28, 1607–1608 (1992).
[CrossRef]

IEEE J. Quantum Electron. (8)

H. Li, T. Lucas, J. G. 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]

N. M. Al-Hosiny, I. Henning, and M. Adams, “Correlation of electron density changes with optical frequency shifts in optically injected semiconductor lasers,” IEEE J. Quantum Electron.42, 570–580 (2006).
[CrossRef]

S. Wieczorek, W. Chow, L. Chrostowski, and C. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron.42, 552–562 (2006).
[CrossRef]

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

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron.21, 784–793 (1985).
[CrossRef]

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

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39, 1196–1204 (2003).
[CrossRef]

T. B. Simpson, J. Liu, and A. Gavrielides, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron.32, 1456–1468 (1996).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

E. Lau and M. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Topics Quantum Electron.15, 618–633 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett.20, 395–397 (2008).
[CrossRef]

A. Daly, T. Gründl, S. Huber, M. Müller, B. Roycroft, M. Amann, and B. Corbett, “Voltage spectroscopy and the operating state of an optically injected long wavelength VCSEL,” IEEE Photon. Technol. Lett.24, 1245–1247 (2012).
[CrossRef]

S. K. Hwang, J. Liu, and J. K. White, “35-GHz intrinsic bandwidth for direct modulation in 1.3- μsemiconductor lasers subject to strong injection locking,” IEEE Photon. Technol. Lett.16, 972–974 (2004).
[CrossRef]

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

J. Lightwave Technol. (1)

J. Opt. B: Quantum Semiclassical Opt. (1)

M. Bondiou, R. Gabet, G. M. Stéphan, and P. Besnard, “Linewidth of an optically injected semiconductor laser,” J. Opt. B: Quantum Semiclassical Opt.2, 41–46 (2000).
[CrossRef]

Opt. Lett. (1)

K. Iiyama, K. Hayashi, and Y. Ida, “Simple method for measuring the linewidth enhancement factor of semiconductor lasers by optical injection locking,” Opt. Lett.17, 1128–1130 (1992).
[CrossRef] [PubMed]

Opt. Commun. (3)

S.-K. Hwang, S.-C. Chan, S.-C. Hsieh, and C.-Y. Li, “Photonic microwave generation and transmission using direct modulation of stably injection-locked semiconductor lasers,” Opt. Commun.284, 3581–3589 (2011).
[CrossRef]

Y. Okajima, S. Hwang, and J. Liu, “Experimental observation of chirp reduction in bandwidth-enhanced semiconductor lasers subject to strong optical injection,” Opt. Commun.219, 357–364 (2003).
[CrossRef]

Z. Jiao, Z. Lu, J. Liu, P. Poole, P. Barrios, D. Poitras, G. Pakulski, J. Caballero, and X. Zhang, “Linewidth enhancement factor of InAs/InP quantum dot lasers around 1.5μ m,” Opt. Commun.285, 4372–4375 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep.416, 1–128 (2005).
[CrossRef]

Proc. IEEE (1)

P. Winzer and R. Essiambre, “Advanced optical modulation formats,” Proc. IEEE94, 952–985 (2006).
[CrossRef]

Other (2)

E. J. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, “Auto-07p: Continuation and bifurcation software for ordinary differential equations,” Tech. rep., Concordia University, Montreal (2007).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, Inc., 1995).

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Figures (9)

Fig. 1
Fig. 1

(a) Photon, S, and (b) carrier number, N, as a function of frequency detuning from the free running cavity resonance for an injection ratio of −27 dB after a numerical integration. The end points of the selected time series signals at each detuning are indicated by grey dots while the maximum, minimum and average of those time series are shown using blue, green and black solid lines respectively. All possible fixed point values of S and N as calculated from the stationary analysis are traced out by a dashed line with stable points marked with red dots. Sfr and Nfr are the free running values of S and N respectively.

Fig. 2
Fig. 2

(a) The range of stable phases as determined from a stability analysis. Under weak injection the stable phase is limited by ±π/2 − arctan(α) whereas at high injection ratios it is limited by ±π/2. Two separate regions of stable phase occur near −51 dB. The minimum phase span is approx. 5π/8 − arctan(α) and occurs near −36 dB. (b) A zoom of the region near −51 dB which has two separate areas of stable phase.

Fig. 3
Fig. 3

(a) Frequency detuning of fixed values of ϕ with injection ratio for selected phases. The limits of the stable locking area (black dots) are calculated through the stability analysis. Hopf (HB) and Saddle-Node (SN) lines are shown in blue and red respectively. (a) At low injection ratios the SL region is limited by ±π/2 − arctan(α). (b) Detuning under stronger injection. The phase condition at the boundaries changes with injection until eventually the SL region is bounded by the ±π/2 line. Other phase curves stop varying in the detuning ordinate.The points marked with red crosses are cusp bifurcation points (labeled C) and codimension-two Fold-Hopf, also known as Zero-Hopf, bifurcation points (labeled FH) [9].

Fig. 4
Fig. 4

(a) Variation in the carrier number with detuning at low injection ratios. The positive, Δω+, and negative, Δω, locking widths as well as detuning at which the carrier number equals the free running carrier number, Δω0, are highlighted for an injection ratio of −58 dB and α = 2. (b) Testing the correctness of | Δ ω / Δ ω 0 | = 1 + α 2 for α = 0 to 3.5. This asymmetry is valid only for injection ratios in the S1 region for each α, as shown in Fig. 2(a) for α = 2.

Fig. 5
Fig. 5

(a) Frequency detuning with injection ratio for fixed ϕ between −π/2 − arctan(α) and π/2 where the phases difference between the chosen ϕ is non-linear. The black dots show the stable locking boundaries. The cross section at +8 dB (upper inset) shows that, under strong injection, the majority of the π phase change happens near the ϕ = 0 point near −25 GHz. The lower inset shows the phase condition on the Saddle Node line smoothly changing from π/2 − arctan(α) to π/2 as phase lines of increasing value become tangent to it. The trajectory of one curve is highlighted by dashing.

Fig. 6
Fig. 6

Plots of (a) phase and (b) carrier number with detuning for multiple injection ratios. The points at which ϕ = 0 are marked with black dots in both plots and always correspond to the minimum of the carrier number.

Fig. 7
Fig. 7

The resonance frequency, fr, of the optically injected laser calculated using a numerical analysis of the system and the frequency difference between the cavity resonance and injected light, |δfres|, at injection ratios of −35 dB, −24 dB and −13 dB. The estimate of fr from |δfres| becomes more accurate with increasing injection strength as the effect of the optical injection becomes stronger than the intrinsic carrier/photon resonance. The value of the free running resonance frequency fr,fr is indicated.

Fig. 8
Fig. 8

(a) The resonance frequency at the zero phase point as a function of injection ratio. At ratios < −35 dB the system retains a resonance at fr,fr. As injection strength increases that resonance drops in frequency to 0 GHz except for a region around 3 dB where it returns approximately to fr. (b) The various modulation parameters at the zero phase point as a function of injection ratio. Where the resonance frequency has gone to 0 GHz the damping rate no longer exists and instead splits into extra two real poles. These branch apart and then recombine at 2 dB where the resonance becomes non-zero again. At higher ratios one of the extra real poles gets very large while the other converges to the frequency of the conventional real pole.

Fig. 9
Fig. 9

The modulation response parameters of the system as a function of detuning for injection ratios of (a) −13 dB, (b) −5 dB and (c) 3 dB emphasizing different configurations of the reals poles at ϕ = 0. (a) The triple real poles smoothly join the damping and single real pole curves together. (b) The curves no longer join and the two of the triple real poles now branch away from the damping curve while the third one continues as the single real pole as at detunings away from the zero phase point. (c) The resonance frequency is nonzero so the damping and real pole curves are continuous and single-valued.

Equations (11)

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d S d t = [ G 0 ( N N t r ) γ p ] S + 2 k S inj S cos ( ϕ )
d ϕ d t = α 2 ( G 0 ( N N t r ) γ p ) 2 π Δ ω k S inj S sin ( ϕ )
d N d t = I q γ n N G 0 ( N N t r ) S
S = I / q γ n N G 0 ( N N t r )
ϕ = arcsin ( 2 π Δ ω k 1 + α 2 S S inj ) arctan ( α )
N = N t r + γ p G 0 2 k G 0 S inj S cos ( ϕ )
Δ ω 0 = k 2 π S inj S f r
Δ ω = k 2 π S inj S 1 + α 2 Δ ω 0 1 + α 2
α = ( Δ ω Δ ω 0 ) 2 1
Δ ω ϕ 0 = α k 2 π S inj S
k = 2 π Δ ω ϕ 0 α S f r S inj

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