Abstract

This work investigates the behavior of a zero-detuned optically-injected quantum-dash Fabry-Perot laser as the injected field ratio is increased from near-zero to levels resulting in stable locking. Using a normalized model describing optically-injected semiconductor lasers, variations in the slave laser’s free-running characteristics are shown to have a strong impact on the coupled system's behavior. The theoretical model is verified experimentally using a high resolution spectrometer. It is found that the quantum-dash laser has the technological advantage of a low linewidth enhancement factor at low bias currents that suppresses undesirable Period-2 and chaotic behavior. Such observations suggest that optically-injected quantum-dash lasers can be used as an enabling component for tunable photonic oscillators.

©2009 Optical Society of America

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References

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  1. T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
    [Crossref] [PubMed]
  2. L. F. Lester, N. Terry, A. Moscho, M. Fanto, N. Naderi, Y. Li, and V. Kovanis, “Giant Nonlinear Gain Coefficient of an InAs/AlGaInAs Quantum Dot Laser,” Proc. SPIE 6889, 68890M.1–68890M.8 (2008).
  3. T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
    [Crossref] [PubMed]
  4. P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
    [Crossref] [PubMed]
  5. S. K. Hwang, H. F. Chen, and C. Y. Lin, “All-optical frequency conversion using nonlinear dynamics of semiconductor lasers,” Opt. Lett. 34(6), 812 ( 2009).
    [Crossref] [PubMed]
  6. F. Mogensen, H. Olesen, and G. Jacobsen, “Locking Conditions and Stability Properties for a Semiconductor Laser with External Light Injection,” IEEE J. Quantum Electron. QE-21, 7 ( 1985).
  7. J. M. Liu, Applications of Nonlinear Dynamics (Springer Berlin / Heidelberg, 2009), pages 341–354.
  8. T. B. Simpson and J. M. Liu, “Enhanced Modulation Bandwidth in Injection-Locked Semiconductor Lasers,” IEEE Photon. Technol. Lett. 9(10), 1322–1324 ( 1997).
    [Crossref]
  9. D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
    [Crossref] [PubMed]
  10. N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
    [Crossref]
  11. F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
    [Crossref]
  12. 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(5), 430–432 ( 2001).
    [Crossref]
  13. A. Villafranca, G. Giuliani, S. Donati, and I. Garces, “Investigation on the linewidth enhancement factor of multiple longitudinal mode semiconductor lasers,” Proc. SPIE 6997, 699719.1–699719.8 (2008).

2009 (2)

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

S. K. Hwang, H. F. Chen, and C. Y. Lin, “All-optical frequency conversion using nonlinear dynamics of semiconductor lasers,” Opt. Lett. 34(6), 812 ( 2009).
[Crossref] [PubMed]

2008 (1)

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

2007 (1)

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

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(5), 430–432 ( 2001).
[Crossref]

1997 (1)

T. B. Simpson and J. M. Liu, “Enhanced Modulation Bandwidth in Injection-Locked Semiconductor Lasers,” IEEE Photon. Technol. Lett. 9(10), 1322–1324 ( 1997).
[Crossref]

1996 (2)

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

1995 (1)

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

1985 (1)

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking Conditions and Stability Properties for a Semiconductor Laser with External Light Injection,” IEEE J. Quantum Electron. QE-21, 7 ( 1985).

Alsing, P. M.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

Chen, H. F.

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(5), 430–432 ( 2001).
[Crossref]

Erneux, T.

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

Gavrielides, A.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

Goulding, D.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Greene, G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Grillot, F.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

Hartnett, M.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Hegarty, S. P.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Huyet, G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Hwang, S. K.

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. QE-21, 7 ( 1985).

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(5), 430–432 ( 2001).
[Crossref]

Kovanis, V.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

Lester, L. F.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

Lin, C. Y.

Lin, C.-Y.

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[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(5), 430–432 ( 2001).
[Crossref]

Liu, J. M.

T. B. Simpson and J. M. Liu, “Enhanced Modulation Bandwidth in Injection-Locked Semiconductor Lasers,” IEEE Photon. Technol. Lett. 9(10), 1322–1324 ( 1997).
[Crossref]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

McInerney, J. G.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Melnik, S.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

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. QE-21, 7 ( 1985).

Naderi, N.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

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. QE-21, 7 ( 1985).

Pochet, M.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

Rachinskii, D.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Rasskazov, O.

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Simpson, T. B.

T. B. Simpson and J. M. Liu, “Enhanced Modulation Bandwidth in Injection-Locked Semiconductor Lasers,” IEEE Photon. Technol. Lett. 9(10), 1322–1324 ( 1997).
[Crossref]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

Terry, N.

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

Appl. Phys. Lett. (1)

F. Grillot, N. Naderi, M. Pochet, C.-Y. Lin, and L. F. Lester, “Variation of the feedback sensitivity in a 1.55μm InAs/InP quantum-dash Fabry-Perot semiconductor laser,” Appl. Phys. Lett. 93(19), 191108 ( 2008).
[Crossref]

IEEE J. Quantum Electron. (1)

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking Conditions and Stability Properties for a Semiconductor Laser with External Light Injection,” IEEE J. Quantum Electron. QE-21, 7 ( 1985).

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

N. Naderi, M. Pochet, F. Grillot, N. Terry, V. Kovanis, and L. F. Lester, “Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser,” IEEE J. Sel. Top. Quantum Electron. 15(3), 563–571 ( 2009).
[Crossref]

IEEE Photon. Technol. Lett. (2)

T. B. Simpson and J. M. Liu, “Enhanced Modulation Bandwidth in Injection-Locked Semiconductor Lasers,” IEEE Photon. Technol. Lett. 9(10), 1322–1324 ( 1997).
[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(5), 430–432 ( 2001).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (3)

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 ( 1995).
[Crossref] [PubMed]

P. M. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, “Lang and Kobayashi phase equation,” Phys. Rev. A 53(6), 4429–4434 ( 1996).
[Crossref] [PubMed]

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection,” Phys. Rev. A 53(6), 4372 ( 1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, “Excitability in a Quantum Dot Semiconductor Laser with Optical Injection,” Phys. Rev. Lett. 98(15), 153903 ( 2007).
[Crossref] [PubMed]

Other (3)

J. M. Liu, Applications of Nonlinear Dynamics (Springer Berlin / Heidelberg, 2009), pages 341–354.

L. F. Lester, N. Terry, A. Moscho, M. Fanto, N. Naderi, Y. Li, and V. Kovanis, “Giant Nonlinear Gain Coefficient of an InAs/AlGaInAs Quantum Dot Laser,” Proc. SPIE 6889, 68890M.1–68890M.8 (2008).

A. Villafranca, G. Giuliani, S. Donati, and I. Garces, “Investigation on the linewidth enhancement factor of multiple longitudinal mode semiconductor lasers,” Proc. SPIE 6997, 699719.1–699719.8 (2008).

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Figures (4)

Fig. 1
Fig. 1 Operational states of an optically injected system; experimentally collected using the high resolution spectrometer: (a) the Period-1 state showing strong relaxation oscillations; (b) the Period-2 state showing both the Period-1 & Period-2 relaxation oscillations; (c) the locked state showing single mode operation; and (d) the chaotic state. For all cases the slave laser bias was 60 mA.

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Fig. 2
Fig. 2 Bifurcation diagrams showing theoretical solutions to Eqs. (1) - (3) for zero-detuning conditions. The three cases correspond to respective P, T, and α-factor values for 60mA, 70mA, and 80mA slave bias conditions and illustrate the dynamic nature of the QDash slave laser’s operational behavior based on bias current. T is the same for all 3 cases, 55.6.

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Fig. 3
Fig. 3 Injection-locking experimental setup.

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Fig. 4
Fig. 4 Experimental spectra associated with the 60mA slave bias case shown theoretically in Fig. 3(a). The injected field ratio values for the individual plots correspond to the experimental bifurcation and reverse bifurcation points, as well as Period-1 and stable conditions. (a) Lower stable locking regime; (b) bifurcation point transition from stable to Period-1; (c) Period-1 regime; (d) reverse bifurcation from Period-1 to stable; and (e) upper stable locking regime. Normalized from 191.914 THz.

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Tables (1)

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Table 1 Numerically Calculated and Experimentally Observed Reverse Bifurcation Injection Field Ratio (η 2) Values

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Equations (6)

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

d E d τ = N E + η cos ( ψ )
d ψ d τ = Δ − α N − η E − 1 sin ( ψ )
T d N d τ = P − N − P ( 1 + 2 N ) E 2
η 1 = ( 1 + 2 P ) ( 1 + α 2 ) 1 / 2 T − 1 ( α 2 − 1 ) − 1 = ( 1 + α 2 ) 1 / 2 α 2 − 1 γ R ≈ 1 α γ R
η 2 = [ ( α 2 − 1 ) 2 P ] 1 / 2 T − 1 / 2 = ( α 2 − 1 ) 1 / 2 ω r ≈ α ω r
0 η exp = ( 1 − R ) R P m a s t e r K P s l a v e

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