Abstract

A rate equation analysis on the modulation response of an optical injection-locked quantum cascade laser is outlined. It is found that the bifurcation diagram exhibits both bistable and unstable locked regions. In addition, the stable locked regime widens as the linewidth enhancement factor increases. It is also shown that both positive and negative optical detunings as well as strong injection strength enhance the 3 dB modulation bandwidth by as much as 30 GHz. Finally, the peak in the modulation response is significantly influenced by the optical frequency detuning.

© 2013 Optical Society of America

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  1. M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
    [CrossRef]
  2. S. Borri, I. Galli, F. Cappelli, A. Bismuto, S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, J. Faist, and P. De Natale, Opt. Lett. 37, 1011 (2012).
    [CrossRef]
  3. B. Meng and Q. J. Wang, Opt. Express 20, 1450 (2012).
    [CrossRef]
  4. C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
    [CrossRef]
  5. T. Erneux, V. Kovanis, and A. Gavrielides, “Stability boundaries of injected quantum cascade lasers,” Phys. Rev. E, submitted for publication.
  6. Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
    [CrossRef]
  7. R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
    [CrossRef]
  8. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
    [CrossRef]
  9. A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
    [CrossRef]
  10. J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
    [CrossRef]
  11. B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
    [CrossRef]
  12. W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
    [CrossRef]
  13. A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
    [CrossRef]
  14. J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
    [CrossRef]
  15. E. Tournié and A. N. Baranov, Semicond. Semimet. 86, 183 (2012).
    [CrossRef]

2013 (1)

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

2012 (5)

S. Borri, I. Galli, F. Cappelli, A. Bismuto, S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, J. Faist, and P. De Natale, Opt. Lett. 37, 1011 (2012).
[CrossRef]

B. Meng and Q. J. Wang, Opt. Express 20, 1450 (2012).
[CrossRef]

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
[CrossRef]

E. Tournié and A. N. Baranov, Semicond. Semimet. 86, 183 (2012).
[CrossRef]

2011 (1)

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

2010 (1)

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

2005 (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

2004 (1)

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

2003 (2)

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
[CrossRef]

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

1998 (1)

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

1982 (1)

R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
[CrossRef]

Atsuki, K.

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

Baillargeon, J. N.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Baranov, A. N.

E. Tournié and A. N. Baranov, Semicond. Semimet. 86, 183 (2012).
[CrossRef]

Bartalini, S.

Bismuto, A.

Borri, S.

Cancio, P.

Cannon, B. D.

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

Capasso, F.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Cappelli, F.

Cho, A. Y.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

De Natale, P.

Destic, F.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

Dhooge, A.

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
[CrossRef]

Ding, L.

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

Erneux, T.

T. Erneux, V. Kovanis, and A. Gavrielides, “Stability boundaries of injected quantum cascade lasers,” Phys. Rev. E, submitted for publication.

Even, J.

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

Faist, J.

S. Borri, I. Galli, F. Cappelli, A. Bismuto, S. Bartalini, P. Cancio, G. Giusfredi, D. Mazzotti, J. Faist, and P. De Natale, Opt. Lett. 37, 1011 (2012).
[CrossRef]

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Filloux, P.

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

Galli, I.

Gavrielides, A.

T. Erneux, V. Kovanis, and A. Gavrielides, “Stability boundaries of injected quantum cascade lasers,” Phys. Rev. E, submitted for publication.

Gellie, P.

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

Giusfredi, G.

Govaerts, W.

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
[CrossRef]

Grillot, F.

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

Hegarty, S. P.

B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
[CrossRef]

Hutchinson, A. L.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Huyet, G.

B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
[CrossRef]

Kawashima, K.

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

Kelleher, B.

B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
[CrossRef]

Kovanis, V.

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

T. Erneux, V. Kovanis, and A. Gavrielides, “Stability boundaries of injected quantum cascade lasers,” Phys. Rev. E, submitted for publication.

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

Kuznetsov, Y. A.

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
[CrossRef]

Lang, R.

R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
[CrossRef]

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

Ludge, K.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Maineult, W.

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

Majer, N.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Mazzotti, D.

Meng, B.

Mollier, J. C.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

Murakami, A.

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

Myers, T. L.

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

Otto, C.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Pausch, J.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Petitjean, Y.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

Scholl, E.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

Sirtori, C.

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Sivco, D. L.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Taubman, M. S.

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

Tournié, E.

E. Tournié and A. N. Baranov, Semicond. Semimet. 86, 183 (2012).
[CrossRef]

Tredicucci, A.

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

Tylaite, E.

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Wang, C.

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

Wang, Q. J.

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

Williams, R. M.

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

ACM TOMS (1)

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, ACM TOMS 29, 141 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

W. Maineult, L. Ding, P. Gellie, P. Filloux, and C. Sirtori, Appl. Phys. Lett. 96, 021108 (2010).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

J. Faist, A. Tredicucci, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, IEEE J. Quantum Electron. 34, 336 (1998).
[CrossRef]

R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
[CrossRef]

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

Y. Petitjean, F. Destic, J. C. Mollier, and C. Sirtori, IEEE J. Sel. Top. Quantum Electron. 17, 22 (2011).
[CrossRef]

J. Appl. Phys. (1)

C. Wang, F. Grillot, V. Kovanis, and J. Even, J. Appl. Phys. 113, 063104 (2013).
[CrossRef]

New J. Phys. (1)

J. Pausch, C. Otto, E. Tylaite, N. Majer, E. Scholl, and K. Ludge, New J. Phys. 14, 053018 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, Phys. Rep. 416, 1 (2005).
[CrossRef]

Phys. Rev. E (1)

B. Kelleher, S. P. Hegarty, and G. Huyet, Phys. Rev. E 86, 066206 (2012).
[CrossRef]

Semicond. Semimet. (1)

E. Tournié and A. N. Baranov, Semicond. Semimet. 86, 183 (2012).
[CrossRef]

Spectrochimica Acta Part A (1)

M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochimica Acta Part A 60, 3457 (2004).
[CrossRef]

Other (1)

T. Erneux, V. Kovanis, and A. Gavrielides, “Stability boundaries of injected quantum cascade lasers,” Phys. Rev. E, submitted for publication.

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Figures (4)

Fig. 1.
Fig. 1.

Local bifurcation diagram of an injection-locked QC laser for LEF values of 0, 0.5, 1.0, and 2.5. Solid line is the saddle-node (SN) bifurcation and dashed line is the Hopf bifurcation. The supercritical bifurcation is denoted by thick lines while subcritical bifurcation by thin lines. The stable locking regime is bounded by the supercritical bifurcations. The investigated laser is operating in the stable locked region of the bifurcation diagram with an LEF of 0.5, where the vertical dotted line indicates an injection ratio of 5.0.

Fig. 2.
Fig. 2.

Main: 3 dB modulation bandwidth as a function of the injection ratio (for zero detuning and LEF=0.5). Inset: related IM response. Note the absence of any peaks.

Fig. 3.
Fig. 3.

Main: 3 dB modulation bandwidth as a function of detuning (for Rinj=5.0 and LEF=0.5). Inset: IM response under various detuning conditions. Note the appearance of the resonance peak under positive detuning.

Fig. 4.
Fig. 4.

IM response for various gain stage numbers increasing from 20 to 40, note that it is normalized to the case with Npd=30 (under zero detuning and Rinj=5.0). Inset is steady-state result for Ibias=1.5Ith. Photon population for the free running laser is SFE7.2×106, and for the injection-locked laser S13.3×106.

Equations (8)

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

dN3dt=ηIqN3τ32N3τ31G0ΔNS,
dN2dt=N3τ32N2τ21+G0ΔNS,
dN1dt=N3τ31+N2τ21N1τout,
dSdt=(NpdG0ΔN1/τP)S+βNpdN3τsp+2kcSinjScosΔϕ,
dΔϕdt=αH2(NpdG0ΔN1/τP)ΔωinjkcSinjSsinΔϕ,
H(ω)=p1p2p3p4p5z1z2z3Πk=13(jωzk)Πk=15(jωpk),
z1=kcSinj/S(cosϕαHsinϕ).
ωR=ΔωinjαH2(NpdG0ΔN1/τP).

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