Abstract

We demonstrate measurements of the α factor of a distributed-feedback quantum cascade laser (QCL) by using a newly modified self-mixing interferometric technique exploring the laser itself as the detector. We find a strong dependence of the α factor on the injection current, ranging from 0.44 at 120mA to 2.29 at 180mA, which can be attributed to the inherent physics of QCLs.

© 2006 Optical Society of America

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  1. J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
    [CrossRef] [PubMed]
  2. T. Gensty, W. Elsäßer, and Ch. Mann, Opt. Express 13, 2032 (2005).
    [CrossRef] [PubMed]
  3. T. Gensty and W. Elsäßer, Opt. Commun. 256, 171 (2005).
    [CrossRef]
  4. C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
    [CrossRef]
  5. M. Osinski and J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987).
    [CrossRef]
  6. J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).
  7. M. S. Taubman, T. L. Myers, B. D. Cannon, and R. M. Williams, Spectrochim. Acta, Part A 60, 3457 (2004).
    [CrossRef]
  8. Y. Yu, G. Giuliani, and S. Donati, IEEE Photon. Technol. Lett. 16, 990 (2004).
    [CrossRef]
  9. C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
    [CrossRef]
  10. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
    [CrossRef]
  11. Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
    [CrossRef]
  12. A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
    [CrossRef]
  13. J. P. van der Ziel, J. Lightwave Technol. LT-7, 347 (1989).
    [CrossRef]
  14. K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
    [CrossRef]
  15. D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
    [CrossRef]
  16. Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
    [CrossRef]
  17. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  18. K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
    [CrossRef]
  19. C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Opt. Lett. 25, 230 (2000).
    [CrossRef]

2005 (3)

T. Gensty and W. Elsäßer, Opt. Commun. 256, 171 (2005).
[CrossRef]

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

T. Gensty, W. Elsäßer, and Ch. Mann, Opt. Express 13, 2032 (2005).
[CrossRef] [PubMed]

2004 (5)

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

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

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

C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
[CrossRef]

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

2002 (2)

D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

2000 (1)

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

1989 (1)

J. P. van der Ziel, J. Lightwave Technol. LT-7, 347 (1989).
[CrossRef]

1987 (1)

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

1986 (1)

A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
[CrossRef]

1983 (1)

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

1982 (1)

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

1980 (1)

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

Alping, A.

A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
[CrossRef]

Andrekson, P. A.

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

Baillargeon, J. N.

Beck, M.

D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
[CrossRef]

Bertilsson, K.

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

Beyer, T.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

Braun, M.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Bronner, W.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Buus, J.

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

Cannon, B. D.

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

Capasso, F.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Opt. Lett. 25, 230 (2000).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Chicharo, J. F.

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

Chiu, L. C.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Cho, A. Y.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Opt. Lett. 25, 230 (2000).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Chuang, S. L.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

Donati, S.

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

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

Elsäßer, W.

Eng, S. T.

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
[CrossRef]

Faist, J.

D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Fuchs, F.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Gensty, T.

Giuliani, G.

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

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

Gmachl, C.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Opt. Lett. 25, 230 (2000).
[CrossRef]

Henry, C. H.

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

Hofstetter, D.

D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
[CrossRef]

Hugon, O.

C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
[CrossRef]

Hutchinson, A. L.

Kim, J.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

Kobayashi, K.

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

Köhler, K.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Lacot, E.

C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
[CrossRef]

Lambrecht, A.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Lang, R.

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

Lerttamrab, M.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

Li, E.

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

Mann, Ch.

T. Gensty, W. Elsäßer, and Ch. Mann, Opt. Express 13, 2032 (2005).
[CrossRef] [PubMed]

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Margalit, S.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Myers, T. L.

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

Norgia, M.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

Osinski, M.

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

Rörgren, R.

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

Sartori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, Opt. Lett. 25, 230 (2000).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Szwaj, C.

C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
[CrossRef]

Taubman, M. S.

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

Tell, R.

A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
[CrossRef]

Tredicucci, A.

Vahala, K.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

van der Ziel, J. P.

J. P. van der Ziel, J. Lightwave Technol. LT-7, 347 (1989).
[CrossRef]

Williams, R. M.

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

Xi, J.

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

Yang, Q. K.

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Yariv, A.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

Yu, Y.

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

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

Appl. Phys. Lett. (2)

D. Hofstetter, M. Beck, and J. Faist, Appl. Phys. Lett. 81, 2683 (2002).
[CrossRef]

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[CrossRef]

IEEE J. Quantum Electron. (4)

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

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

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

J. Kim, M. Lerttamrab, S. L. Chuang, C. Gmachl, D. L. Sivco, F. Capasso, and A. Y. Cho, IEEE J. Quantum Electron. QE-40, 1663 (2004).

IEEE Photon. Technol. Lett. (1)

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

J. Lightwave Technol. (3)

A. Alping, R. Tell, and S. T. Eng, J. Lightwave Technol. 4, 1662 (1986).
[CrossRef]

J. P. van der Ziel, J. Lightwave Technol. LT-7, 347 (1989).
[CrossRef]

K. Bertilsson, R. Rörgren, P. A. Andrekson, and S. T. Eng, J. Lightwave Technol. 11, 1147 (1993).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A, Pure Appl. Opt. 4, 283 (2002).
[CrossRef]

Opt. Commun. (1)

T. Gensty and W. Elsäßer, Opt. Commun. 256, 171 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

C. Szwaj, E. Lacot, and O. Hugon, Phys. Rev. A 70, 033809 (2004).
[CrossRef]

Proc. SPIE (2)

Y. Yu, J. Xi, E. Li, and J. F. Chicharo, in Proc. SPIE 5628, 34 (2005).
[CrossRef]

Ch. Mann, Q. K. Yang, F. Fuchs, W. Bronner, K. Köhler, T. Beyer, M. Braun, and A. Lambrecht, in Proc. SPIE 5365, 173 (2004).
[CrossRef]

Science (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sartori, A. L. Hutchinson, and A. Y. Cho, Science 264, 553 (1994).
[CrossRef] [PubMed]

Spectrochim. Acta, Part A (1)

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

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Top, calculated SM signals with the same feedback strength, but different α factors: (a) α = 0.25 , (b) α = 1 , and (c) α = 2.75 . Middle and bottom: Experimentally obtained normalized waveforms from the signal of (d) a HgCdTe photovoltaic detector and (e) from the voltage drop across the QCL. The time intervals required for the determination of the α factor are also shown in (e).

Fig. 3
Fig. 3

Measured α factor as a function of the injection current of a DFB-QCL. The threshold current is I thr = 115 mA . The inset shows the dependence of the carrier population of the upper (N3) and lower (N2) laser level on the pump parameter R P = I I thr .

Equations (1)

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α = χ r n χ i n .

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